You'll eventually need to go the sewer path to get to The Old Sewers, which is much harder than the first sewer level, so you can get to The Watcher, who is the second boss.

The mutations are always the same, but you will find blueprints for more of them. The mutation's stats will upgrade with the scrolls you pick up if you choose the color of the mutation you're using.

As for what to unlock, that's going to be personal preference. Personally, I think that most of the weapons are dogshit, but others seem to enjoy many of them that I don't. You'll want to unlock all of the base upgrades like the health potion and the gold saver, but that will come in time.

As for speedrunning, I don't care for it. I'd much rather clear a level than rush through it for a few extra cells. Some people like speedrunning. I am not one of those people.