Jump into quick match, and just mute anyone who is rude using the instant buttons. HotS is a lot friendlier than other mobas and overwatch, but still has its fair share of dicks.
In terms of playing, few things to note about human players versus AI:
1) the AI stops chasing you quite early, human players will chase more to secure kills, so you will have to back out earlier to survive
2) AI players often hang around way too long before retreating, whilst human players will move more and go back earlier, so it's harder to get initial kills
Just jump in. It should be fine. Just stick to QM till you get a better hero pool since the draft modes mandate having a large one.
Thank you both for the advice, I think we will jump in tonight!