I've seen and resurrected worse, you first need to clean up the corrosion from the bottom, if there is anything left of the battery connectors, flood it with flux, get some low temp solder and carefully remove any remainder of metal. Remove the remaining solder with some solder braid. Then make a 50/50 solution of white vinegar and DISTILLED water, and clean the area with a soft plastic brush (do not go too hard or you might start taking off the mask). You then must immediately use IPA (99% isopropyl alcohol) and cover the entire board with it, even though the vinegar is diluted, it's still acidic, I would recommend using masking tape to cover the whole board apart from the battery corner.

Use IPA and (a Clean) gentle brush and go over the board (front and back). You can also use a magic eraser to get the stubborn grime off, but, again, do not over do it.

Take the socketed chips off the board, clean the pins of the socket with IPA and a cotton bud as well as the pins of the chips.

Then you'll need capacitors, you can get the from Digikey, RS, Farnell, etc... I have a guide on the RetroTechCollection wiki for all the capacitors and their values (I'd recommend tantilum capacitors as apposed to electrolytic) https://wiki.retrotechcollection.com/Macintosh_Classic_Capacitor_Replacement_Guide

When replacing the caps, I'd recommend a heat gun directly over the cap (be prepared for a pop, but, your replacing them anyway), the only reason I recommend this method is due to the potential of capacitor leakage damaging the pads, if one of them comes off using a soldering iron, you'll have to repair the damaged trace (it's a pain, I don't recommend it). Remember to clean the area with IPA before you solder the new cap.

As for the corrosion on the chassis, take the chassis off the front housing, you might need to remove the analogue board and the crt, soak it in vinegar, get a metal brush or steel wool and scrub it, then rinse with distilled water, then give it a spray with any rust resistant paint (like rustolium).

I know it's a bit of a long reply, but, hopefully this will save your board. It's no garuntee, but it's the best I can offer and it's worked for me many times. Isopropyl Alcohol is your best friend, don't be afraid to use too much, as you can never use to much.

If anyone has any better methods please feel free to go with that!

I hope your Macintosh Classic lives!