Advice needed - replacing ancient brakes on even more ancient MTB?

I'm completely new (yesterday!) to the whole maintenance/mechanical side of bikes, so I might get a few of the technical terms completely wrong. I apologise in advance.

I have a question for the more mechanically inclined of you.

I have this really old MTB that I got second hand well over 15 years ago. The previous owner had changed the brakes/shifters but other than that it is still as original as it was when he bought it. And I have never changed a thing except the brake cables once.

I'm only using it to get around town, so I don't need anything fancy or new (in fact, old is better because it won't get stolen) and I really love the bike. So what I want to do is slowly start to change the components, prioritising by need.

The rear brake cable is starting to fray and rust and needs to be replaced soon. But since I've got those ancient caliper brakes it's always a b*** to do. So I was thinking of not just replacing the cable but the whole rear breaks and putting V-brakes on the thing. But I'm not sure if that would work.

Do I need to change the brake levers too? Will the new V-brakes fit on my old frame? What do I have to know?

I have some pictures if you need them.
I hope one of you can help me out here.

I don't know if you can do so on all mtbs, but we have done so on at least one. You'll need new brake levers too, I think, because v-brakes pull more cable than calipers. New brakes are cheap, even cheaper if you buy used. Go for it. Reviving old bikes is so much fun :-)

PS. If you have a mtb with v-brakes already you can check, by just switching over a brake and seeing if you can get the brake pad to hit at the right spot. Brakes are really easy to move around and adjust, if you just pay attention to what you're doing and take pictures every now and then it's hard to do anything wrong.

Thanks for the fast reply. I'm absolutely going for it. I'm just wondering how much at once I'll have to do.

Theoretically, I could take the V-brakes off any of the other bikes in the bike room of our building, but I'm not sure I'd make any friends there.

The thing is that I have just learned that my brakes are called cantilever and not caliper...that might make a difference...

yup, I meant cantilever too. That's what we've switched.