At a minimum you need to get it a recap done and remove the batter and replace with a coin cell one. This isnt an option, it NEEDS to be done. I cant tell you how many A1200 and A4000 I have had in over the last couple months that are just near beyond saving because the previous owners didnt want to bother opening them up and making sure they were okay. If its never been done, its NOT okay.
RAM is maxed at 16MB and will require 4X 4MB 72 pin simms. If its a non CR model without the CPU soldered onto the MB you also will have a 2MB simm for the chip RAM. The CR model with a 68030 soldered to the board has 2MB of chip soldered onto it. I havent ever done the 64MB RAM hack to those CR boards and am not sure if it can even be done.
The 64 MB hack requires me to desolder some chips and add a repcement programmed for the hack as well as cutting or socketing a chip and adding some tape under the socket to isolate the signals normally cut. Both wats are fine, it just depends on your preference.
If you want more RAM you will need a ZII RAM card or a CPU card with more RAM slots on it. The BigRAM+ can still be found for a good price if you look. I got mine for cheap at Amiga Kit and it adds 256MB. They are currently only $90
http://amigakit.leamancomputing.com/catalog/product_info.php?products_id=1129If you need a recap and the clock batter upgrade done just let me know, or you can visit my site in my signature. Just be prepared to wait a bit for it to be done. I travel for work a lot and get to them in the order I receive them. I have a few ahead right now waiting on me to get back on Friday. A simple recap with no required repairs only takes me a couple hours to do.
As far as power supply goes, I can also replace the internal fans with a better quiet one. Its not a lot of work. Its also easy to adapt an ATX supply, but finding one that fits well is a challenge at times is all. I can recap them as well and if they are in working condition thats a better option.