Unless your customers need 8xAA and 16xAF, here's what you'd want in a LAN gaming centre computer for a decent budget.
Athlon64 3200+
Any Nforce 3 or 4 mainboard...I would recommend an a8n or Neo4 Platinum for stability, if not OCing too hardcore
1gb of ram (1024mb is the sweet spot with AMD boards right now, it doesn't have to be high performance ram. Just get some corsair VS, overvolt it a LITTLE BIT and see if you can get some decent timings out of it)
A single sATA HDD will do, recommend Samsung's 120gb model for low noise and heat (becomes a big issue with lots of computers in one room)
nVidia 6600GT OR x800XL - the definite price-performance sweetspot right now for video cards. If you really want, a 6800GT is better, but you pay for having the latest and greatest, so to speak
The case and PSU don't have to be super expensive. Get a sleek, clean, tidy case (ie ABSOLUTELY NO VIPER GAMING CASES) and a reputable 400+ watt PSU. If it's a decent brand (read: Vantec, OCZ, thermaltake, Enermax, Ultra, etc) then you don't need a 500+ Watt beast.
I recommend a CORDED MX518 gaming mouse (used one myself, feels and performs well) - cheap too and pair it with a decent wired keyboard (logitech is good stuff)
As for monitor, 17" LCD is a good size, just make certain it has Digital (DVI) input and 16ms or better response time. Samsung, LG, and Sony all make excellent LCDs in this range, but if budget becomes a problem, BenQ is a decent up and comer as well.
Another thing - since it's a LAN centre, make sure the rooms are well ventilated, and that each computer has at least an extra 120mm or a pair of 80mm cooling fans installed. If you don't, you will have very high ambient temps in the room and inside the computers, which equals instability (trust me, lol). This is imperative if you plan OCing at all as well.
Good luck with your LAN centre, I have many a time entertained thoughts of opening one, but that costs $ and time.
By my quick and somewhat overestimated quote, that's about $1500 Canadian - or about $1200 American. Perfect
EDIT: Plus $25 ish for a pair of headphones I guess, but that's overestimated a bit, I just tallied it up without checking actual prices. I'm building a system similar to that, though, since it will run any currentgen game very well.