New Project

Rear axle spacing for an '80s frame will be 126 mm, which will take wheels of the period up to 7 speed block, not the more recent 8 speed through to 11 speed cassettes, which fit on 130mm wheels. If you want to build a fixed bike, you would be better off looking for a frame with 120mm rear spacing and either horizontal dropouts or track ends.
Or get 6mm worth of spacers to fit between the cones on the axle and the frame.

Brazings (if present) for brake levers will be standard fit.
You will most likely have to drill the rear of the fork to accept a recessed nut on a modern calliper.

Also be weary that the frame was probably designed for 27" wheels and you will probably go for a nice new set of slightly smaller 700c wheels, therefore you'll need to make sure the brake calliper arms can reach the new rims...

Make sure you have all the required tools to do this. Set aside money to buy a decent chainwhip and lockring tools for the future. Also invest in good tools.

A few useful threads to get you going:
http://www.londonfgss.com/newpostinthread3372.html
http://www.londonfgss.com/thread4716.html?highlight=toolbox

Yes! Hit my daily '1 useful post' quota for today.