Need Tire Advice - A Little More Street

I don't know if this is the right place to post this, but I've decided to take my trusty 1998 Gary Fisher Big Sur a little more road and a little less "any place I want to go." I'm realizing that it's been probably 15years since I've done any really serious mud/rocks and with having gotten my 7y/o twins bikes for their last birthday I'm spending even more time puttering around the neighborhood, and I feel like some more street oriented tires might be a good step.

Now me, I'm a 6'4", a little over 270# powerlifter that even on the road has a tendency to hop over, into and onto lots of things that I probably shouldn't. The bike came with relatively good parts/well built for someone my size (and for the late '90s), and I've broken relatively little the way it is when I used to ride much harder with only modifying the RockShox (don't remember the model) for my weight (at the time 290-300) mostly with custom springs and dampers. It's running WTB Velociraptor tires (Which were OE on this bike) VERY knobby front with a knobby rear almost paddle tread. AWESOME in the muck. Not great for the street, really fairly terrible. FWIW, they're labeled 26 x 2.1" wide and the front measures exactly that, the rear is slightly narrower.

I'm looking for something smooth rolling, preferably MUCH faster/lower resistance on the street (I want to put some real miles on this thing), but I don't want to give up any width/sidewall both because of my size and my tendency to do stupid things (my assumption is that a wider tire will take more bouncing around/off of things before I hurt it). What I'm finding is that a lot of stuff labeled in this size range 50-559 to 57-559 (roughly 26x2 - 2.25) with street tread tends to run very undersized.

Any suggestions for tires? I'd like to keep things fairly cheap for now since I'm not sure how well this is going to go. Am I wrong in wanting to stay with a fatter tire? FWIW, I don't know what the widest tire is you can mount on a standard rim but measuring the frame I don't see even a 2.5" wide tire hitting anything.