Right on Mauxe, those are all solid champs especially for starting out in their respective roles.
Annie - She'll allow you to last hit cause of her Q's ability to refund mana. Most AP mids seem to be balanced around being given the blue buff which probably won't happen in your games for a while. It can be very difficult to last hit with an AP caster when you run out of mana cause of your weak auto-attack so Annie will be a great mid to learn.
Ashe - She'll teach you how to position. AD Carries when played optimally are glass cannons, and people who start out with the ones who have great escapes like Graves, Corki, Ez, etc learn bad positioning habits. Positioning in LoL is defined by doing the most damage possible without dying/taking too much damage in return. If you wade into a fight with Ez and get blown up but escape, you might think that you played okay since you survived but if you team didn't survive along with you, this might not be the case. If you play Ashe, if you get focused/caught you will die but this is almost a good thing. If you're the ADC you should not be getting caught out by the other team, you should not be close enough to the enemy bruisers to get mauled and Ashe will teach you this fine line to walk. She also has her fantastic ultimate which will allow you to initiate a team fight if you don't happen to have a good tank initiator on your team, which will unfortunately happen sometimes. People in this game get way too caught up in lane counter picking and don't focus enough on team synergy but anyway...
Garen - No mana, no energy costs, naturally tough, has sustain. Great "My First Solo Top" but you might get bored after a while.
Master Yi - Kind of a great pub stomper champion but as far as I know he hasn't really found his place in the meta yet, but season three is just starting so he might end up as a great jungler. In the meantime, if you have a good game with him you will have a lot of fun playing him.
Ryze - An interesting champ as he will teach you the joy of smartcasting, having a high damage dealer who is also very tanky, and he also has the possibility of becoming a late game hyper carry like Yi does.
Just finished writing all of this and realized it probably looks like its written in a foreign language to you! Good luck with your new champs anyway...