I'll try to keep things concise here:
1- you can definitely replace the quill stem and 25.4 bar with a quill-to-threadless adaptor, new 31.8 stem, and 31.8bar. However, this would be needlessly expensive, and weigh a lot. you'd likely need a shim for the stem, too. Better to run what you've already got, or get a new stem and bars if you like. There is a quill stem with a 31.8mm clamp out there; a friend of mine used it on his old litespeed, and it actually looks alright. If it were me, I'd either clean up the original stem/bars and run those, or get some nice bits from nitto.
2-As others have kinda said, you'll need long-pull levers to run v-brakes. Personally, I think V-brakes are more awesome than Cantilevers. However, many MTBs from the cantilever era have cable routing that is optimized for use with centerpull cantilever brakes, and if that's the case with your frame, I'd scrap the v-brake idea and just tune up the cantis. A picture of the brake cable routing on the top tube by the seatpost would help us determine what we're dealing with.
3-take your wheel out and measure the distance between the drop-outs. "Looks to be" isn't as precise as "measured at". If it is indeed 135, any q/r mtb wheels will do. If it's 130 or 126mm, you might want to get a set built up around some road hubs, like shimano tiagra or suchlike, to run the modern cassette.
4-Your BB shell is english threaded, or "bsa". Basically, any of the common shimano mtb Bottom brackets will fit, from square taper to octalink to the somewhat new outboard-style hollowtech II. That will be no problem; you'd need to run some of the included spacers if you're going with hollowtechII. Depending on which cranks and the width/angle of your chainstays, you may have clearance issues. This isn't likely if you're running a "standard" mtb triple, with the 44/32/22 rings, but something you should be aware of if you're thinking about running some less-typical cranks.
**Above, someone said that sram x7 and Shimano stuff won't work well together. In my experience, assuming we're talking about 9speed stuff, it'll work fine so long as you're running the sram rear shifter and the sram rear derailer, OR the shimano rear shifter with the shimano rear derailer. The cranks, chain, cassette, front derailer, and left shifter will all play nice between sram 9speed and shimano 9speed. With the 10speed stuff, Shimano decided to screw the pooch with some aberrant cog spacing, as well as with derailer pull ratios. If you have ten speed stuff, you may wish to revise your componentry.
hth
-rob