Do different game types earn different amounts of gold?
I'm not earning a lot of gold at the moment. I realize this is probably to be expected since you can buy your heroes with cash, and that's likely what they'd prefer, but right now I'm getting about 10 gold per win. But I've only played coop versus bots, not in competitive matches.
Do I earn more/less gold with different game types?
Yes.
Cooperative games earn you 10 gold if you win.
Quick match games earn you 20 gold with an additional 10 if you win.
The bulk of your gold is going to come from daily quests and hero/account level gold rewards.