Fairly certain it won't lag. I own a LCD screen and my PS2 doesn't lag on it.
I don't know if they have wi-fi.
Basically, we want to build up a tab there as they already have a system of payment per hour for their setups. Building a tab means we could lower the cost later or contribute to their arcade as pure profit. Either way, we want to make a lasting impression with them, that's why we want to keep the 5 dollar standard.
I'm inviting, at max, 15 people and expecting about 8 of them to show up. Could be more or less, but I am shooting for more. Also, we only have 1 PS2. If we had more, that'd be 14 dollars an hour; which needs a turn out to warrant that kind of commitment.
@Riotblade: Again, the time is subject to change. Since the place is open till 1 AM, it's negligible to change the time unless the PS2 provider can't make it.