Keep in mind I'm assuming you're playing on a level 4 account or something, and you're just trying to get a feel for each individual role. Some of these champs I suggest are expensive (6300 IP), but are well worth the investment. In saying that, don't buy them now, play them when they roll around in free week. Nothing worse than buying a champ, not clicking with it and having it sit there idle for the next year.
My recommendations would be:
for your cheap and easy characters (450 IP each, not particularly hard combos)
From there it depends what kind of AP mid you'd like to 'specialize' into I guess. You can go burst assassins like Katarina, Ahri, chunky mages like Swain or Diana (although she is both, stupidly enough). All these type of champs will be more expensive though, so I'd still recommend learning the cheap basic ones. Annie is a walk in the park, crazy easy to snowball and farm with her.
Warwick is extremely safe, you should never really drop low in your jungle at all, and his ganks are easy post level 6. Skarner is more of the same, but his ganks are a little bit better pre-6, but he is again strong overall and has a game-changing ult. I put Maokai in there because he is very, very easy to gank with. A simple root and knockback and it's typically a kill. There's a bit more to him than that, but obviously you'll pick up the intracacies as you go along.
I would avoid champions like Lee Sin and Shaco, even though they both can be great junglers, they need to get a roll on early or it's a no-go for mid and late game. They also have slightly more complicated abilities.
By far the most common top lanes you'll face. In saying that, you don't NEED to know all of them; just learning Irelia for instance is good enough, or Jax. They can pretty much make it with the majority of the top laners, and they are always strong choices. There's other weird paths you can go down, like Vladimir top, but honestly he is more difficult than them.
Taric is faceroll. Literally nothing to him but a walking stun, a bit of burst and a heal. He works with EVERY ADC in the game, and nothing on him is hard to master, but he's always a safe pick. Blitz is harder, but he's fun to play and you feel like a bit of a champ landing good grabs all day. Sona / Janna are another 2 that are good, but a little bit more complicated as they're generally squishy. You sound like you want to try Blitz, so give him a go I'd say.
Any of these 3 work well with every support. Then there's 'the rest', like Ashe, Miss Fortune, Varus, Caitlyn etc, but they generally aren't as strong in all matchups. In saying that though, they're perfectly viable, and Ashe is one of the easiest to play and is cheap. She's a good place to start, but I'd recommend trying these 3 at some point.
Of course, people will suggest different champs in every position, but I feel these picks are generally 'safe' and are some of the more enjoyable characters (after having tried them all out). Best of luck with everything, and remember that at low level it's a bit of a clusterfuck with everybody going everywhere, so don't worry too much about picking correct positions.
Out of your champs I would take:
- Blitzcrank (try Taric!)