Any estimates on how much wire ground braid a person should order for such a game? - Will depend on the game. Get yourself a ball of yarn (or string). Lift the PF and trace the wire with it. Then you can pull the yard off in one piece and measure it. Then add some extra to that length to be safe for any mistakes made.
Should I get the 1/4" version or the bare wire twisted version? - Should be the twisted wire for the insert and gi Lights. Check the game to be sure but though.
Also, do I need any additional hardware that taps into the wood (I believe they are Tnuts?)? - Yes, there will be several T-nuts. Be advised they most likely wont be the same size. You can get them at a local hardware store so you can just wait till you get them out and have a chance to measure the thread sizes.
The playfield is already drilled as it was an original that was restored. - Was it drilled after being cleared? If not you will need to chase the holes with some nice new drill bits. This is because clear will get into those holes and make them smaller. Not doing this increases your chances of cracking the clear when installing things. Easy to do, just measure the hole from your old PF (slide a bit in the hole to match the right size) and go slowly. I like to countersink the holes as well. May be unnecessary but it sets my mind at ease. I just one of these. Light pressure for 1-2 seconds is all that is needed.
20310 3pc countersink bit set.jpg
Also, just checking on the sockets... could those just be rock tumbled to clean up once detached? Yes - I use crushed walnut shells in my tumbler for them. Be advised it can be a pain to get all the shells out though sometimes Also, watch to make sure the spring doesn't come out. I've had that happen a couple of times when tumbling sockets. I'd pick up a dozen or so new ones just to be safe and replace ones that don't clean up well or aren't nice and tight when a light is put in them. Cheap insurance in my opinion.