For the Radeon 9600 XT, $250 should be about the regular price, rather than a sale price. I bought a Sapphire card (from
Genitech) because it had 256MB RAM for the same price as most other 128MB cards (though the core/memory clock speeds are slightly lower).
Intel's
D845GRG product description says it has an AGP slot (4X, 1.5V), which is compatible with the
Radeon 9600 series. Gateway may have a version of the board without an AGP slot, but I would expect the model number to be different in that case.
You definitely need a new power supply if you are going to be adding a graphics card (or much of anything else). Check the case and see if there is physical room for a power supply about time and a half or twice the size of the one in there now (I'm pretty sure it is just a baby PS). If there isn't, you would have to move everything to a new case. A 300/350W power supply would be about $50-70, while a case and power supply would be range from $50 to about $160. A cheap case is OK, but you don't want to skimp too much on a power supply.
I would check the pricing on RAM to maybe double what you have (256MB is about $80 and 512MB is $150). There may be two 128MB pieces of RAM in your system rather than one 256MB piece, so you might have to replace one rather than add more.
The video chip takes 61MB off the 256MB of system RAM, and Windows XP takes a good chunk of what is left, so a memory upgrade should be noticeable and helpful in most applications.
You can put up to a 2.8GHz CPU in that motherboard, which isn't really worth the effort unless you can get a good deal on it. The speed boost would be noticeable, but probably not significant enough to justify a couple hundred dollars. If you are going to be holding onto that system for awhile, I'd consider checking prices occasionally and upgrading before compatible CPUs are discontinued.
I'm not sure what kind of performance the 82845G chipset has, but as long as it is at least competent, the memory may be more of a bottleneck than graphics.
A new motherboard and the associated upgrades would likely go over $500, so I think your options are to either upgrade the RAM and hold on until you can afford something better, or be more aggressive and upgrade the power supply (and maybe case), RAM and video card. The latter option costs more, but will help your system last longer before you can not run a game you really want to play.
Except for Thief 3 (and maybe other upcoming games) you could increase the RAM first, and see how much it helps performance. If it is 'enough' to help with what you are playing now, then you can put off upgrading the video and power supply. Upgrading everything should let you play Thief 3, though with not much headroom with the CPU (I don't know how conservative their requirements are, so it could be fine or you might need to turn down a few settings to get acceptable performance).