I've run Avon Road Riders, Bridgestone BT-45, Dunlop & a host of other cheap slippery tires.
When I had my first VT Ascot back in 1988, Dunlop was the #1 street tire. What an incredible difference over the original tires! When I returned to bikes a few years ago, Avon & Bridgestone were talked about often. I tried the Avons & think they're great. I have the Avon RR's on my FT Ascots & the BT-45's on my VT Ascot. Both are real good vintage bike tires, but I think the Avon is a bit nicer & stickier tire. The Avon Road Riders are what I plan to standardize my bikes on whenever it comes time to replace tires.
As far as wider tires... I don't think our bikes would benefit any. I like to run the most narrow, low profile tire that I can get away with for better cornering. My FT/CBR hybrid has a 130 series tire in the rear & handles real well. My other Ascots have the modern equivalent of the original tire sizes.
When shopping around for an online source of tires, I found that Amazon.com had the best price on a pair of Avons. It was just shy of $200 with free shipping. Of course you should give your local Cycle Shop a shot at it, especially if you need a Shop to mount & balance your tires.
That's about all that I can think of adding. I think there was an earlier attempt at a tire thread, but it didn't take off.
J.