You've got a few things, well, not wrong but not quite correct.
Top needs to be self sufficient. Because it's the farthest spot from the Drake Pit (which historically is highly contested during the laning phase) it's the lane least likely to be visited by most of the rest of the team. That doesn't mean no one should ever visit, but that in regular play, there probably won't be as many high points happening around Top as around Mid or Bottom. Champions who regularly go top have some way to heal or shield themselves on a respectable (if sometimes costly) cooldown. Jarvan, Shen, Garen, Maokai, Renekton, Rumble, and Trundle all carry that self sustain with them when they cover top lane. A focus on top lane play is staying in lane as long as possible using what you can in your kit to survive. If you're not there to grab that minion gold and exp, no one will be, and that's no bueno.
Mid is one of the positions with wide options. Most Midlaners bring wave clear (a quick clear of the minion wave from a safe position) and burst damage. That's not the end all be all though, as Champions like Karma, Orianna, and Lulu regularly mid, not to mention options like Katarina. Generally, a Mid Laner should bring a few of the following: Wave Clear, Burst, Utility, and Roaming Potential. Good Wave Clear is important though, as clearing your wave and moving for a roam or objective take or just threatening either is playing smart for a mid laner. It's why the two Energy based Assassins, Akali and Zed, are split between Top and Mid Lanes. Akali normally goes Top because she has sustain but poor wave clear, and Zed goes Mid because he has no sustain but quality wave clear.
Bot Lane Carries all share two common factors; excessively high sustained damage in the late game and a very high threat against enemy Towers. Some have good wave clear, some don't. Some have maneuverability, some don't. A majority of them eventually purchase Item builds that let them wreck a beefy tank Champion no matter what items it's carrying. A noticeable thing about Bot Carries is that when they do have a repositioning tool, they can use it in any direction. Champions like Ezreal, Corki and Lucian (mostly played Mid now), Caitlyn, Ziggs, and Tristana all highlight this. If they don't have a repositioning ability, they likely have some form of movement speed boost, ala Sivir, Jinx, Twitch, Miss Fortune, and Draven.
(You'll notice I brought up Ziggs as a Bot Lane Carry. The lane favors him, believe it or not. Having a dedicated support peeling for him keeps him safer than the generally safe lane of Mid. As well, considering all of his Abilities are AoEs means his damage is more of a threat in bot lane as it's 100% more enemy champions to hit than he would find in Mid. Bot Carries have to have Tower threat, and his Satchel Charge can auto-kill a Tower if it is low enough.)
Support is a role that revolves around Utility. What form that utility takes depends on the Meta and the champion kit, but the generally have at least one form of Hard Crowd Control (most everything that isn't Slows) and all use Mana as a resource. There is likely no wider pool of play style options compared to any other position. You protect? Soraka, Janna, Braum, Lulu, Tahm Kench. You attack? Annie, Leona, Brand, Zyra. You do both? Sona, Karma, Nami, Alistar, Morgana, Thresh, Rakan. So on and so forth. No role has had as many champions played on the professional scene as Support. What Supports DO though is set up or secure plays for their teammates. A single Sona ult, Tahm swallow, Leona engage, or Morgana shield could make or break an entire team fight. A focus on TRADITIONAL Support Champions is that their power doesn't get significantly stronger with a high amount of gold COMPARED to other types of Champions. Instead, they invest their Gold and Items into empowering their team more, with Items like Aegis of the Legion, Redemption, Mikael's Crucible, and Ardent Censor. Because of their low Gold power, not much relative strength is lost if they buy a Sightstone item, and doing so greatly increases the team's safety and power because vision control is soooo important.
So finally, we're at Jungle. The biggest things a Jungler needs to bring is at least a decent Jungle clear (most champions can reach this actually), but more than that, more than anything, they need to have Engage. Almost entirely from out of vision too (as in, from over a jungle wall). Of all the 'regular' Junglers, only 5 have no way of crossing a wall without using Flash. And those five bring other strengths to make up for it. Rammus and Nautilus bring a large amount of CC and hazard, Olaf and Udyr bring a nice amount of dueling potential, and Nunu brings a buff for auto attacking allies and one of the most obnoxious Counter Jungling playstyles you can end up against. Ivern is basically the 'Oddman Out' in regards to Junglers, but he makes up for it by bringing an equal amount of Utility and a counter jungle potential that can rival Nunu.
All that doesn't explain EVERYTHING ever, but it does give a crash course I think. I hope I was helpful.
, or a champion that is good at ganking.
Jungle now) and the META will shift again.
Bruisers and juggernauts who have a balance of durability, attack and ability damage tend to build Black Cleaver. These champs have high base damages that scale with level, and moderate scaling if they build damage items.
AD assassins who burst squishy targets from up close tend to build Lethality (i.e. Serrated Dirk upgrades). Strong enough to be a kill threat to squishy or low-health targets unless behind, and are very deadly when ahead.
Champs that invest heavily in critical strikes deal very high damage with their basic attacks, generally focused on sustained damage through numerous auto attacks. Until they buy 2 or 3 items, their strength is weak to moderate.
Champs who buy lifesteal have powerful auto attack power, which is turned into sustain by buying items like these. If a champ who builds these gets ahead, they are going to be very deadly and very hard to kill.
Champions who buy Trinity Force are attack-focused, and generally use abilities to empower their attacks or weave frequent ability casts with auto attacks. Their power spike is generally felt in the mid-game.
