>>1644124rj the bike guy on youtube has good tutorial videos
sheldon brown
I don't know why you think you'll be better of blindly modernizing it. All you'll do is waste money, and run into compatibility issues.
the tyres should have have their size listed on them. What does it say?
V-brakes are not the 'newer version' infact, cantilever brakes were raced in CX for far far longer than v-brakes ever had any high end relevancy.
Pic related is the brake pad you want, in Salmon or dual compound preferably. Thinline or no is fine. Smooth post cantilever. Kool stops.
Clean and grease the fastening bolts in the brake when you install, and make sure the arms pivot smoothly.
If you want v-brakes, you'll need new levers as well.
Cut the grips off. Slide the new ones on with isopropyl alcohol.
Those derailers are not dangerous. What you should do is replace the chain, and while you're at it, unbolt the derailer cage and clean the jockey wheels.
Work out if you infact have a freewheel or a cassette.
https://www.sheldonbrown.com/free-k7.html It's probably the former. You can repack it, but i would rather just replace with a new tourney unit, if it's gummed up, and if that won't cause suntour indexing problems (is it indexed or friction).
If you don't replace it, do clean all the cogs before you put a new chain on.
the bigger bearing jobs will be your bottom bracket, wheel hubs, and headset. They might not need doing, but do check. I'd also remove the seatpost and stem and clean and re-grease them. And re-cable the bike.