your primary damage dealer should be the Assassin. Dragon rank him up, and mushroom him ASAP. Literally no other character can match his dps
Just tried. Both shroomed up, 14 dragon shards for Assassin, 12 for Golem, the price is now about the same, maybe I could put Assassin at 15. But Assassin's DPS is e80, while Golem's is e118. I didn't expect such a big difference, but my first choice was right :)
Now I need 1.1e6 shrooms for the best upgrades and earning 4e4 per reset at lvl 1600 :(
Edit: actually the Wizard is the best when you can buy him his last upgrade. He has a total 2000 multiplier. Phoenix will be the best DPS as soon as I can get him lvl 1000: 11250 multiplier.