but I'm looking for some of those champs who don't really get a spotlight and are actually quite good.
Most champions in LoL are balanced enough you can easily get to gold by just putting in the time and effort to learn them inside and out. If you're a reasonably casual player or starting out, pretty much any champion is going to work if you put in the time.
I'd recommend focusing on a champion where you like their aesthetic and play-style and just get good using them. If they aren't one of the top meta picks you might get some flack in champion select, but you'll usually get a solid advantage vs. your opponents by knowing exactly how to deal with every meta pick - where they won't be nearly as solid with dealing with a more exotic pick.
Most of mastering a champion comes from knowing exactly how powerful you are vs. your opponent and what shenanigans you can get away with - allowing you to make aggressive plays and side-step their power spikes with great precision and ease.
Riot's balance is solid enough that the minor %advantages or disadvantages you'd get from playing a strong or weak pick don't mean much if you have a lot more skill/experiance on a given champion than your opponent.
I need a champ who can just handle laning solo if need be.
Pretty much every champion with a Fighter classification works much better alone than they do in a group, and you'll be fine in a 1v1 situation with pretty much any of them.
A few mages, marksman, supports, and tanks also work well in a solo lane.
Do I save up for a 6300 or is there a nice "economy sized" champ that fits the bill?
IP costs are only a reflection of when a champion was released, not their power level. There's plenty of old champions that remain quite relevant in any given meta - if you look at all the top picks of any given season the release dates of the top picks are usually pretty random and don't play favorites with recent champions/release dates.
I'd recommend just purchasing a lot of cheaper champions and building up from there unless one of the 6300 champions really catches your attention. It will allow you to test out more rolls and play-styles right away, and isn't as sucky when you find you really don't like a certain champion's style.
Also - for being self-sufficient or just experimenting with a lot of play-styles at once, 
is a really solid pick.
She's pretty much every class packed into 1 champion with her 4 skills, she's really self-sufficient and can lane just about everyone adequately as well (even appearing in tournaments as a top-lane, jungle, mid-lane, and support pick).
