I shall also vote for the Blizzard 1230IV if all he's going to do is games.
Most important though is having fast RAM. I did a small, unscientific test (as in just a rough idea) with a small prime number program compiled under GCC 3.4 (I think) on OS3.0 and simply adding fast RAM to an A1200 gave it a huge boost. Slightly more than a 50MHz 030 could alone (as in chip RAM only). The card I used was just a RAM expansion board, still using the A1200s 14MHz EC020.
The 030 plus fast ram was a lot faster still
Prime numbers from 1 20001, displaying each prime as it went (I timed it with a stopwatch):
A1200 Stock: 1m21s
A1200 4MB FAST RAM: 57s
A1200 030 50MHz Chip RAM only: 59s
A1200 030 50MHz 16MB FAST RAM: 38s (as far as I can remember)
So I think that if you was really on a budget and couldn't even stretch to a Blizzard 1230IV, just adding Fast RAM will give you a much quicker machine.
Still, it will be interesting to see what an 040/25 makes of this when I get my BPPC soon :-) I've also just downloaded vbcc and am going to try m68k and later PPC from that. For a laugh!