I was skeptical of Overwatch at first coming from TF2 myself, but its actually really good, lots of fun! I would say you wanna be a little trained in all characters so if you need a particular skillset for the group, you can jump in no problem. Some good starting characters in my opinion are:
Soldier 76: pretty much straight run and gun and he can heal himself with an AoE effect that can help allies as well.
Mercy: healing very similar to the medic from TF2. Pretty straight forward.
Roadhog: pretty good tank that can stun people with his chainhook and heal himself, if you know how to play him right, he's pretty damn good.
Reaper: just run and gun with some shotguns, and if you get into trouble, you can just "ghost" away.
I've only been playing a few months, but those are what I started really, now I play a little of everything.