Wall of text inc. :P
No problem; again bear in mind that this is all just my opinion, like you I feel like I'm much better at talking about the game than actually playing it :P. A lot of these opinions though are formed based on stuff I learned watching lastshadow9 (you can find him on youtube, twitch, facebook, etc. he also sometimes goes by the username imls, I'll link you some stuff at the bottom) stream/play/coach, he's a coach for many professional teams over the years and is high ranked in Korea solo q. Here are some of his recommendations for champions; again, not champions you have to or should play, but just to give you an idea of some of the simpler champions he recommends (the list changes a lot, but just some examples):
Top: Maokai, Lulu
Jungle: Vi, Master Yi
Mid: Orianna, Lulu
ADC: Graves, Caitlyn
Support: Leona, Morgana
Again, not champions you have to be playing (I only have three of them in my pool, and I kind of disagree with the Maokai/Lulu pick, but of course he knows more about the game than I do, lol), but just to give you a sense of some other champs you might want to look into, etc.
So I'm not particularly struggling with playing the champs at all. I actually do pretty well with some of them like Anivia or Irelia. My problem isn't the champions, it's the number of champions haha.
Yea, so my opinion still is if you want to stick to a small number and really start to master their mechanics, sure; be wary it might actually limit you in a sense (I played AP Midalee since I was very low level even, she's the champion that I learned how to hit skillshots with, but I've had to go back and relearn how to play mid lane because I fell into some bad habits only playing Nidalee, and honestly can't really hit other champion's skillshots as reliably since Nidalee's spear has a pretty unique speed, width, range, etc. lol), but this is why you pick a few champions per role instead of just one. Again, if you feel like you have a grasp over certain champions, ignore what I'm saying and go practice, lol, but the goal (imo) is to be so comfortable mechanically on a champion that you don't even have to think about what you're doing with controls, you're thinking about what you want or need to do in a game and doing it just instinctively almost.
Also general advice is to pick which roles you want to focus on and then start to branch out; I was largely a support main for a long time, but had an okay understanding of mid lane from playing Nidalee/Gragas when he was strong, plus was decent mechanically on mages from playing support mages, so I added mid lane to my roles. I played a ton of Jinx when she came out, Tristana was my first main champion way back when I first started the game, and I mained ADC for a lot of S4, so that's also in my roles. I suck at top lane which is why I'm going with the Bronzodia Malphite (I also play Mundo but he just gets destroyed by Morellonomicon right now), and also Wukong (he's fairly simple, but most importantly he's a comfort pick for me. Still probably going to play more Malphite over Wukong in case I have to fill). Wukong jungle is a similar story; just a comfort pick; I'm still learning Vi.
Top: Yeah, I've worked on both for laning phase. I've beaten most matchups with Irelia from Nasus to Lissandra. So who would you suggest for me to pick in the top?
Again, Irelia/Renekton are great (I would actually track down Sir ArmaMalum on Boards and ask him about Renekton; he's a Renekton main, he knows much more about the champion than I do), Lissandra is also really powerful, but I suck with mages in top lane so I can't give you many pointers there. If you really like AD Nidalee top (like, actually enjoy playing her and not just jumping on the bandwagon like I've seen a lot of players do), go for it. Poppy I know nothing about, but I'm pretty sure she's pretty nuanced and not really a champion you randomly want to pick up unless you plan on investing a lot of time figuring out her nuances (plus she's getting reworked in the near future). You can also play Pantheon; he also is pretty good in jungle and can be played mid.
Jungle: Amumu I'm actually not sure about using, I think I'm just going to drop him. Evelynn I'm definitely going to keep. I really enjoy using her and I have some great success using her.
I had success with Amumu last season but generally have dropped him this season; I'm just not too confident with his sustain issues, etc. Again, if you want to stick with Evelynn, go right ahead, I've just heard she has a lot of issues right now. I haven't seen a Kha'Zix jungle really succeed at my elo (~Silver), and I don't play him so I can't say too much about that. I've seen some good Skarners, though. I personally think jungle Nidalee is a passing fad, but I might be wrong (lastshadow also thinks she's an unstable pick). I would especially recommend easier champions for jungle since there's just so much you have to do; it's the hardest role in the game imo. Vi and J4 are always good (I like Vi more personally; J4 can be fun too, and double as a top laner); Xin Zhao, Warwick (he's getting a rework in the near future), Master Yi, and Udyr (can be a little tough, but he's the champion I first learned to jungle with) are easier junglers to pick up imo; Wukong has some early sustain issues, but he's a champion I enjoy playing and am comfortable on. Honestly if you're looking to learn how to jungle, I highly recommend watching Nightblue3's stream and watching his guides on youtube, very informative if you're looking to pick up jungle, offers good general advice that applies to every champion (so it'll still apply for you even if he thinks Evelynn is really weak right now)
Mid: I really have fun with Anivia. Everyone else I'm still learning and constantly rotating. Again, suggestions?
I'll be honest, I really have no idea about Anivia; I've played her a few times and she doesn't seem that complicated, but you also want to consider your ability to perform on these champions when under pressure (for example, I don't think Twisted Fate is too difficult a champion to play mechanically, but I asked lastshadow about this on stream one time and he laughed at me, lol; his pick-a-card under pressure while having medium-higher ping is a nightmare to use, just as one example. Similarly, hitting Anivia's stun and wall seems like something that's really easy to mess up under pressure). Again, a lot of this comes down to comfort and playtime on a champion; I hit a lot of Nidalee spears that I know if I were playing any other champion, I would have missed that skillshot by a mile. Yasuo, Cassiopeia, Azir are three of the most complex champions in the game imo, I would stay away from them, unless, again, you really want to put tons and tons of hours into learning them. AD Nidalee and AP Nidalee are basically completely different champions imo, I would be wary of that if you decide to stick with her.
For suggestions to try out: Orianna is a champion I really enjoy playing, she can be a bit tricky mechanically at first, but she has a lot of strategic depth that I really enjoy. Annie is good, she struggles against some long range champions though (note: learning how to micromanage Tibbers in a fight really helped me learn how to split my attention to control Orianna and the Ball, which also applies to Azir. Again, not that I recommend playing Azir, but an example of how mastering easier champions can help you learn more difficult champions). Kayle's a bit of an unconventional pick, but I'm learning her in order to deal with melee assassins. Ryze and Veigar (and Mordekaiser) are getting reworks in the near future, so I'm keeping an eye on them. Talon is great if you want an assassin. You can also play Lissandra. Also maybe look into the lesser picked champions, like Malzahar; I've heard he can be really strong. Morgana mid is also being picked in Korea; I don't think she's great at finishing off kills but her ratios are pretty high and her waveclear with W maxed is insane.
ADC: Ashe has been my fav ADC ever since I first played her.
I think Ashe is very underrated as a champion; she could use some buffs but at low elo everything is viable if you know how. I also think she's really fun. Vayne and Kalista are two of the most complicated ADCs in the game imo (up there with Ezreal, Corki, Draven, etc); if you're struggling with orb-walking especially don't play these champs, lol. Other champions to look into: Graves, Caitlyn, maybe Sivir (she's pretty unique as an ADC), Jinx. Tristana is still being tested after her rework, so I'm unsure about her. Varus is also somewhat similar to Ashe in that he has a CC ultimate; he's also a non-meta pick, but again, everything is viable in solo q if you know how lol.
Supp: ok :)
Yea, Nami is super complicated, lol. Taric is also getting reworked in the near future, I'm looking forward to that. Karma, Morg, Annie, Soraka are also good.
OVERALL I still recommend picking up roles and champions slowly; don't try to learn all of this overnight. Most of the champions in my current pool are champions that I have a lot of experience on in the past and just happen to also be pretty simple; really the only champions I've had to learn somewhat recently are Orianna, Kayle, Caitlyn, Vi, and I had to relearn Annie.
Lastshadow's Twitch stream: http://www.twitch.tv/imls
He has links to everything else on his twitch stream if you scroll down; and his ask.fm page; he answers a lot of general questions on here, I would pay more attention to his youtube coaching videos since he talks more about the game on those, where his stream is mostly to watch him play: http://ask.fm/lsxyz
Nightblue3's Twitch stream; he also has links to everything if you scroll down: http://www.twitch.tv/nightblue3
While on Twitch you can also search Scarra or Bjergsen for mid lane, Annie Bot if you want to learn Annie, Geronimo or imaqtpie (he's going to start doing instructional videos on youtube now too) for ADC, and Krepo for support; just some of the streamers I've found helpful, though you can certainly go look for others, professional players you respect or like to watch, etc.