Dating and relationship issues?

Hey all. So first off, i broke up with my girlfriend of ten months a week ago and it went pretty bad. I knew it was going to be hard and i prepared myself for it but i still felt guilty about the whole thing. To be honest, i had been unhappy in the relationship for about three months prior but i kept wanting to see if i could make it work for me. So about three weeks ago, i met this girl who i quickly became smitten with. I know it sounds bad, but it was kind of the thing that gave me the guts to man up and end my relationship. I don't regret doing it, but i know i should have ended it sooner and i could have handled it better but i can't change that now. Anyways, since the breakup, i have been trying to get to know this other girl better and it's not going too bad so far. I know she is attracted to me and that she finds me interesting. So the other day, i went to her apartment and we talked about what was going on and made out for a bit. I really like this girl but i can't help but shake the idea that i shouldn't be dating anyone since i just ended it with the person i was with. I feel like a dirtbag because the situation makes me look like a player but thats really not who i am. This other girl doesn't hold it against me but i still feel bad about it. Anyways, the other thing is that she wants to keep it casual but i'm really not sure what that means. Does she not want to be with me? And am i being a jerk by trying to go out with this new girl so soon? And should i feel bad about the breakup? It's all kind of confusing so any help would be appreciated. I expect to hear some pretty nasty things said about me but maybe someone out there can sympathize and actually offer good advice