It's best to get a few under your belt quickly so you can switch depending on what your team needs.
Healer: Lucio is ace - easy to figure out and your main job is to follow your team around/give them speed boosts so it's a good way to watch how the characters work and get to know the maps. He's best to make yourself useful with early on - and I'm still using him most now. Played well he's a huge asset to any team.
Attack: Soldier 76 is just a run and gun type and is the easiest to get your head around. He's quick and can heal himself though so he's really useful.
Defence: Torjborn is handy because no one likes turrets. But unless you get decent with him it hanging around repairing them and putting them up can be a boring way to play. Junkrat is more fun: playing him well basically boils down to spamming grenades to wherever you think the enemy is or is likely to want to go. You can do amazing damage, rack up kills and be an absolute pain in your enemy's arse with minimal effort.
Tank: Reinhardt is easy to get to grips with. It's hard to get kills with him and make the most of his abilities but being a massive walking shield is useful for any team. Sometimes getting him into the capture point/by the payload and putting your shield up is enough to win the day as he can take a lot of shit before he goes down. Alternatively Bastion in turret mode can be utterly devastating. Wandering around trying to find a good spot to fire from is a good way to get to know the ways in and out of the capture points too.