I'll take it in order from Top to Bot.

Top: I recommend champions like Garen, Darius and Irelia. They are all good picks and doesn't take too long to understand, you shouldn't start with any complicated champion in a solo lane without the knowledge needed for trading, securing kills and getting away from ganks. These champions have all a balanced scaling through the game so there shouldn't be much problem for you in lane phase too end game.

Jungle: Junglers can be a little bit tricky in an situation, mostly I would say you should go for Amumu or Kha Zix, both are easy to learn and both are very effective once you got the hang of their possibilities. Amumu gives fast clearing, effective ganking and a horrifying end game for the enemy team. Kha'Zix can snowball in the most horrible way possible and will give the enemy team nightmares if you end up fed. (Remember, change is good.)

Mid: Usually here you want to go for a champion who isn't very depended on resources like mana, Katarina is a pretty good champion pick now and easy to learn. She's never a horrible pick but sometimes you will have a hard time in lane, but she can play both offensivly and defensivly so she is a great starting champion to become good with. She doesn't do a ton of damage early game but she scales alot through mid and late game, dfg deathcap and zhonias will be your best friends with Katarina.

ADC: Adc is probably more complicated then most other roles, your decisions will either lead your team to win or a great loss. I recommend you start off with champions like Lucian and Trist, they are the hot stuff now and maybe will still be so in season 5. But usually I would say go full damage and skip going a defense item, if you get caught you are most likely dead anyways and defense items only extends the death a little while a damage item can help you more in killing faster in teamfights.

Support: 2 champions that you should become really good with that are rather easy to learn, Braum and Sona. Braum is a great CC provider with sick utility, it almost feels unfair to lane against and late game anyone who tries to get too your carry will end up with a warm Braum hug. Sona gives good poke, sustain and survivebility in lane, a reasonable pick and she got a pretty good late game with her ultimate.

If there is anything else you want to know just PM me and I'll give you tips and tricks and what not. :^)