As a relatively new player myself, I am still learning the champs and their abilities. I have my favorites (Darius for top lane, Annie for AP mid, Fiddlesticks for jungling, etc.), but I do try to set aside some time to play each free-to-play champ in a custom game vs. bots. This helps me figure out if I like playing them and helps me understand their abilities so I can better counter them in normal PVP matches. Custom bot games are also convenient because you can experiment with combos without upsetting teammates and quit the games without penalty after 5-10 minutes if you have to.
If I find a champ I like, I search out guides on Mobafire, LOLKing, etc. I then practice against bots to get the timing, combos, and moves down. From there, I try to spectate a few games where I see the champion being played. After that, I may hit a Co-op vs. AI game or go ahead and try my hand in a PvP match.
Obviously, all of this depends on the amount of time you have to commit to the game. Best of luck to you, and I hope you find a good ADC or bruiser that suits your play style. They certainly are a lot of fun!
P.S. I highly recommend spending the $5 at Gamestop (if you can) to get the starter card. It unlocks a set of champions and gives you an IP and XP boost.