With 6 to 8 machines I would run two 20A dedicated circuits to power the machines. This topic has been talked over many times here but 3 to 4 machines on a 20A circuit is about the right number.

As far as number of machines into one outlet it really doesn't matter it is more about the power going to that outlet. So for example if you wanted to use a power strip in an outlet you could plug 3 or 4 machines into that power strip and all would be fine. Just use a decent power strip NOT one for someplace like the Dollar Store!

Personally I prefer switched outlets for our machines. So instead of an outlet being live all the time each of our outlets is on a light switch. So I can turn off power to all the machines buy just turning off a few light switches. I don't turn machines on and off this way it just makes me sleep better at night to know there is no power going into old arcade & pinball machines when they are not in use.

I agree 15A would work for up to 4 machines but for a couple dollars in wire why not do it right to begin with and run everything for 20 amp? Also with 20A he will not be maxed out if he decides to add a couple more machines or wants to run something else on the same circuit. The only true cost difference between 15 and 20 amp is the cost of the wire. Outlets and breakers basically cost the same either way.

And talking about outlets - I am a big believer in using heavy duty and not the cheapest ones. Again for a couple dollars more you can get something that is safer and will last longer.

I don't see why not - most arcades did things that way back in the day. Start up will create a short term load but I don't think that would cause any issues unless you maxed a circuit out with more than 7 or so machines. Basically the off/on switch on the cabinet is cutting the power to the machine so doing it on the wall instead really doesn't change anything.