it makes me sad that a year latter a player is still considered new, isnt lv 30 yet, doesnt have many champs, or runes.... riot should really address the new player problem of trying to catch up to anyone having played this game for a good length of time.... well... that being said....
i would suggest taking a look at the older lower cost champs.... they are not as evenly matched against newer champion's kits but many of them are easier to use and learn many good fundamentals on....
ashe is cheap, has recently had her kit reworked and is a great champ to have in your stable... learning to last hit and position when you have no implicit escape
amumu can fill many roles, good price, good kit, good team fighter, a great champ to learn how to jg or tank and when to back off from a fight... or initiate
nunu- i dont always care for him but he has point n click abilitys, can go into many roles, and teaches about short range threats
annie - powerful, able to be used mult roles, fun, good to learn as a burst mage, or an ap support ( or even a top lane, stuns = escapes)
morg- yes please.... on so many lvs, yes pls... a lane pushing champ, stuns-4-dayz, support, team fight, and teaches you to learn and manage your cool downs
sion- great champ, strong, tanky, can fail at farming and still make great impact, teaches a lot about ability interactions and combos
because she is the music in the silence, the yin to the adc yang, squishy, 1 shotted, but unkillable.... she will teach you positioning and patience with adc's, as well as proper utilization of complicated ability interaction when played skillfully, and can spam abilitys until skill is obtained
just a brief list but all good suggestions, also i would say create 2 rune pages one for AP one for AD, both can share yellow armor (9), both can share blue scaling magic resist (9), get penetration runes for either ad or ap, and the quints.... this will save some IP on runes by utilizing them in both generalized builds, and a lil defense is always important on all champs...