Originally Posted by veganbikes

Once you get the old grease out of shifters I would do a very light light lubricant and very small amounts. Sometimes if you can figure out a way to get some heat inside without damaging the outside or any plastic or rubber bits you might get the grease loose enough to not need to be removed.

I would make sure to remove everything that is threaded or is bolted into or onto the bike and make sure it is cleaned and greased. Do it before you start riding the bike because knowing you have a stuck seatpost or bottom bracket or something is best to know right away because you may have a better chance of remove it before it gets even worse or to strip what you can now and get rid of the bike.

In terms of Rear derailleur if that is a short cage RD-5500 which is what it looks close to that would be a max 27t cog and max chain wrap at 29t. You might have some luck extending that a scosh with a Wolf Tooth Road Link (I did it on my old 7400 Rear Derailleur and it actually works ok)

For info on vintage parts VeloBase.com is my go to for a lot of this stuff but Shimano has a lot of tech docs for older stuff still on their site: https://si.shimano.com/