The two wax caps are in the phono preamp. Those should be replaced.
The pyramids may or may not be good. Like I said, if you don't have a way to test them for leakage, you should probably just replace them.
The two 50uf electrolytics are part of the bias network for the power tubes. Replace them. No need for anything fancy, plain electrolytics are fine.
I guess the ceramic disk caps don't usually go bad. You can leave them in and listen to the amp with them. See how it sounds. You can always replace them with something else later.
There are also a couple of small electrolytics on the phono preamp tubes. You might want to replace those as well.
Don't forget that new can cap on top.
It can get pretty tedious desoldering resistors and checking everything. Just take your time. Sometimes when the carbon resistors get to much heat from soldering they can drift and not come back down. I'd take out all the caps first then start checking the resistors. They usually recommend changing them if they are 10% or more out of spec. I tore everything out and started from scratch, so I didn't check all of mine.
I can't tell if you did or not, but you should use a ring terminal on that new ground wire. Crimp it then solder it. Use some steel wool on the chassis where it will attach to the transformer bolt. This will ensure a good connection.
I'm sure we'll hear back from you before then, but once you get all the new parts in, do a resistance check first, then when it gets powered up, do a voltage check. I can scan the manual for this if you don't have one.
Here is a link to the
Eico Schematic and one for the
Sam's schematic.