If that were mine, I'd probably only change the rear mech for a dx one. I caveat that with the following.
I'd check anything with a bearing. Hubs, bottom bracket and headset. If they are all good, I'd still probably remove, clean and regrease. Who knows when it was last done, and by doing it, you'll know it has been and fresh grease and a clean will mean everything will spin smoothly and last longer.
Remove anything that can get stuck over time. BB for sure (though if it works, I'd pop it back in after cleaning out the BB and threads, and use copper slip so it will come out again in future).
Stuck seat posts are another thing, pull out and clean it and the inside of the seat tube.
As someone has mentioned, those old quill stems can often get rusty and stuck. Remove, clean and put back in with a bit of copper grease on the threads and maybe the wedge.
In fact anything with a thread can have a dab of copper grease. I would.and always do, even down to the bottle bosses. If there are any open threads for racks etc, buy some nice bolts and fill those holes to prevent ingress of anything.
Brake pads - newer rubber will be better at stopping. I'd get the insert style ones as on good v brakes, but that's just me, canti versions aren't as common as have no threaded part like on v versions.
Tyres, well if yours are ok grip wise and are supple, use until they need replacing. Not impossible, but decent retro looking amber walls aren't as easy to get as you'd hope.
If the grips are still grippy and not cracked or loose, I'd stick with them until they need replacing but depends on condition I guess.
Old cables and outers won't be your friend in the shifting or braking game.
Chain wear, rear cassette wear and front cog wearing worth checking. If things are worn or your chain is stretched, you may need to replace more than just one item.
Those old shifters may have old grease in them. Worth a tiny spray of wd40 to loosen it it. Don't go crazy, you don't want to flush it all out, just add a bit of lubrication to loosen it all up.
That's all I'd do
I'm all seriousness, I would, but if it ain't broke yet, don't fix it until it gets to a point it needs it.
