Reasons NOT to buy a used groupset

A current 105 will almost surely be much better. A lot of improvement happened in those two decades. Even 105 is now 11 speed. Even though the top manufacturing processes with the stringiest tolerances may not be used for 105, it is still manufactured very well and uses good features introduced later. It will allow modern cassettes with larger gear ranges, for example.

Also, even the top DuraAce product can become worn after 25 years of use. Pivots can be loose and wiggling and you would have to have the derailleur in your hands and properly test it. It can be in a very good shape, because they are durable, but it is unlikely to be generally better than a current 105. There are still limitations that keep the cost down - one of the well visible ones is the use of pulley wheels with bushings, instead of ball bearing ones, but 105 receives many features previously introduced in higher-level DuraAce and Ultegra.

Your additional questions: 1. the wheels are unlikely to have a hub that supports modern 11-speed cassettes. You would need a new freehub. 2. I have no idea about Campy.

Twenty-plus year old STIs that really and truly have much life left are rare and expensive.

The 7700 STIs are much more serviceable than most, hypothetically. They allow some make-one-good-one-from-two-bad-ones type stuff to be done where it's not practical otherwise. In practice most of them are trashed by now.

The wear parts on pre-Escape Ergo are all replaceable, hypothetically. In practice the world is getting dry of a lot of that stuff.

You ask about derailleur performance in particular. The age per se isn't what matters, but rather how worn it is. A slopped out RD-7700 is garbage compared to a new RD-R7000. Comparing apples to apples, NOS to new, it's hard to get away from giving a subjective answer there in my opinion, but few reasonable people would find anything to complain about either way. 7700 is longer wearing. More reasonable questions would be what are your gearing needs and do you want something closer to period-correct.

The bike is aluminum, 37 years old, and has a 126mm freewheel hub. It's got light construction for its time in terms of tube choice but it also has monster dropouts. If you want to change the group you're buying a 130 wheel, and then you're going to flex its axle and/or add to the already-considerable chance of frame failure. People do all of those things and it can result in a rideable bike. Whether you want to is up to you. You're buying a Campy wheel if you want Campy and Shimano otherwise. Meanwhile the freewheel hub you've got is one of the nicer ones ever made.

If just getting STI on the Klein is what you really want to do and you're more or less happy with the gear range you've got, you could consider keeping the cranks and wheels, getting new 2x8 STIs, a new 7-speed Shimano 11-28 freewheel, an 8-speed chain, a Claris or Sora 8-speed double front derailleur, and whatever pre-11-speed-road Shimano rear derailleur you want. Running 8-speed STIs as 7 is fine and was once condoned by Shimano themselves.

Finally, there are some Kleins that epitomized the 80s crit-geometry-on-everything trend. If your bike is like this, ie sub-405mm chainstays, then getting the FD rub-free can prove tricky no matter what you do with a more modern group.

Focusing solely on Campagnolo compatibility: if you get an 8-10s Campagnolo groupset, it will require a different freehub body than Shimano wheels. In fact, 8s Campagnolo groups may require a different freehub standard than 9s and subsequent groups (although all 9s and later Campy groups except for the current generation Campagnolo Ekar use the same freehub standard, whereas Shimano has at least two standards in play). Unless you are a Campagnolo aficionado, this could be a reason to avoid Campy.

That said, I believe you have a 7s freewheel, which should imply 126mm rear spacing. I think that you do need a new rear wheel anyway if you upgrade to any more modern groupset; all are designed for 130mm spacing at the rear.

Back in the day, some manufacturers may have taken Shimano cassettes and modified them to have Campagnolo spacing. This was not a common thing. I think Wheels Manufacturing was one of the companies that did this. You can't run a 9s or 10s Shimano cassette with a Campagnolo group and get great results. It may shift, but the shifting is likely to degrade over time. The difference in cog-cog spacing and the total cassette height is just too different between the systems. With 11s and higher, the issue goes away, because there just isn't that much room at the rear for the systems to differ in either of the two parameters I mentioned.

Assuming the chainrings are in good condition (no shark fins etc), can I expect a 25 year old derailleur to operate smoothly enough to be happy with it? Or will I be better off spending the same money on a new Shimano 105?

Three reasons to consider:

• Cassettes and chains are wear parts. Why would you install anything but new? Otherwise you may need to replace the chain in less than 1000km and the cassette has an unknown history so it might be so worn it works with the used chain but no longer works with a new chain.
• If someone is selling a complete bike, they might have bought a new bike with for example slightly different frame geometry. Not that alarming. Although in some cases the reason for buying a new bike could be that the old components are worn. If someone is selling a lot of used components, the reason might be that one of those components is worn out and the rest need to be sold due to not being compatible with new stuff. That's very alarming.
• Removing and installing a large number of components on an old bike requires lots of labor. Especially if one of those components is the rear freehub (you probably have a freewheel hub as opposed to freehub in there and freewheel hubs are not compatible with Shimano cassettes) and especially if the frame spacing is anything other than 130mm or 135mm (you might have 126mm spacing on your frame). If the frame is aluminum and has 126mm spacing, forget it! Steel can be cold set. So what I'm saying here is that if installing all the stuff requires lots of labor, it might make sense to install new unworn stuff as opposed to old badly worn stuff. The time it takes to change the rear hub alone is worth 80 euros to me and might require 18 euros of spokes if the old ones aren't the correct length, so would I install a new hub (20-60 euros depending on if it's thru-axle or QR, disc or rim, etc) or a used one (probably half the price)? Of course a new one.

Should there be any issues fitting these relatively-newer components on my old frame and wheels?

Yes.

Modern Shimano cassettes require a freehub for 8-10 speed systems or 11-speed systems (plus spacer) if 8-10 speed cassette, and specifically require a freehub for 11-speed systems if 11-speed cassette. Your rear wheel has probably a freewheel hub.

If you're very lucky the frame spacing is 130mm. You might be able to find a hub that fits there, although changing the hub in an existing wheel requires quite many hours and wheelbuilding expertise. If you're unlucky the frame spacing is 126mm or less. Then you need to cold set your frame. If you're very unlucky the frame spacing is 126mm or less and the frame is made from material other than steel so it can't be cold set.

is there an easy adjustment I can make to use the Campagnolo groupset, or will I have to buy Campagnolo wheels to fit it?

I don't know anything of Campangolo. My understanding is that Shimano is higher quality and lower cost.