Pre-30 you're really looking to build up to tier 3 runes once you can buy them. Tier 1's are really cheap so slot those in until you can get tier 3 (skip tier 2). AD + magic pen marks, armor seals, MR glyph, and AD or AP quints are good generic sets depending on whether you're AD or AP.
Here are some inexpensive champs that aren't that hard to use in their role. All are 1350 IP or less:
Top: Garen/Nasus/Tryndamere/Mundo/Teemo. Nasus is more farm oriented, Mundo is also very tanky and pretty straightforward. Everyone hates Teemo lol. His mushrooms double nicely as wards for objective control and he can bully in lane.
Mid: Annie/Ryze/Kayle/Morgana/Twisted Fate. Strange is that there are no inexpensive assassin-oriented mid laners (unless you count Alistar with a sheen, which is actually pretty hard for assassins like Zed and Kat to deal with due to his ult, but his WQ is touchy). Annie is a true burst mage.
Jungle: Nunu/Warwick/Fiddlesticks/Chogath/Xin Zhao/Amumu. Nunu is suited to counter-jungle and is pretty safe/sustaining, Fiddle can do it w/o runs and has a nasty team fight ult + okay ganks, Xin deals a lot of early damage and Warwick is something between Nunu and gankers. Amumu is for team fights.
ADC: Tristana/Sivir/Ashe Positioning is everything with ADC. Of these 3, the only one that's pretty straightforward is Trist due to her easy escape; there aren't many good cheap ADC. Spell shield requires experience with champions to realize their tells for spell shield, and playing Ashe against mobility champs/assassins will feel like you're running 100 meters dragging a car tire unless you're used to ADC positioning.
Support: Annie/Soraka/Janna/Taric/Morgana. Annie is a burst mage all-in type here too, while Soraka is more of a poke + heal bot. Janna is good all around as a support with a strong shield and nasty disengage. Taric is probably the most aggressive cheap support, along with Alistar. Morgana is really good too due to how devastating it can be to get hit by her bind in a 2 man lane + strong shield.
All of these champs should be reasonably easy to pick up and play without minding their special mechanics much. The exception is Sivir, where spell shield is rewarding but requires experience to use effectively. I don't recommend Sivir for beginners but you have so few cheap ADC options to try.
Take advantage of free champion rotations to get experience with champs you don't have too.