These days 700c is still the most widely available range of tyres and rims for general touring/trekking.
But if your frame just won't fit a 700c/622mm set-up...
--650A: 590mm bead seat: A lot of old mixte and roadster bikes would have been 650A, or 26 x 1 3/8" as it's better known in the UK. Not much choice of tyres these days, rims almost non-existent. I'd steer clear unless you prize originality.
--650B: 584mm bead seat: lots of 28-40mm road tyres with enough tread for a bit of rough. Still pretty niche, with a lot of whitewall 'Eroica/Porteur/Rene Herse' stuff around, though there are plenty decent mountainbike tyres arriving, but they wouldn't fit a road frame. This size is definitely growing in popularity on both the MTB and touring fronts with rims and mudguards available too.
--650C: 571mm bead seat: the next size down from our 700C wheels. Pretty much dead in adult bikes, restricted to under 23mm tyres and tubs these days, although they do still have a solid following in racing handcycles. Tyres and rims restricted to racing bike widths.
So, a Mixte frame originally built for the dead/dying old UK size 650A/26 1 3/8"/590mm built for a 28mm tyre (646mm OD) could be replaced with previously-dead-but-now-rising-again French 650B/584mm wheels and slightly fatter 32mm tyres with only a small adjustment to the brake block...3mm down and some nice hammered aluminium mudguards. Just watch the frame width between the forks & stays.
A summary of sizing for clarity; the best size guide is the bead seat diameter (ETRTO). Assuming you're not thinking of tubular tyres, this is the diameter of the seat in the rim where the tyre sits, not the outside rim diameter (which is about 12mm larger). Add 2x the tyre width to this number to give a rough estimate of the overall wheel size to check clearances, brake drop etc.
All the best,