Here are a few things to watch out for, to save some money;
1. Don't waste money on a high-end case. Its simply a metal framework to hold every thing else. These days you can get a decent "mid tower" ATX case, even one with a built-in 120mm fan, for under 40 bucks U.S. Dollars (without power supply).
2. Don't waste money falling for that "more ram is faster" mantra. Its not true. You only need enough ram to run the OS, and the game you are playing. In general, 3 to 4 Gigs is just fine. Anything more and it will probably be an expensive waste. I play a LOT of games, Call of Duty 4 (MW 1 and 2), BioShock2, Fallout 3, Gears of War, Half Life 2, TFC, etc, etc. I have 1 Gig of ram in my system (its running XP). That's right, ONE gigabyte of ram. Games run just fine on my system. Besides, unless you use a 64 bit OS, your computer can't see any more than around 3.4 gigs anyway. I would not run a 64 bit OS right now, not just for a gaming rig, because the driver support isn't where it needs to be. You don't want to pay extra for that OS only to find out your motherboard's USB chipset isn't supported.
3. Don't opt for the fastest hard drive you can find. You don't need a 10,000 RPM raptor drive, or an SSD drive to play games. once the game loads a level, it doesn't really rely on the hard drive that much. A simple 7,200 RMP drive is fine. Like the others have said, 500 Gigs is minimum if you want to load up a lot of games on there. Some games can take up to 25 Gigs, like Starwars: The Force Unleashed.
4. Don't spend more on your graphics card than you spent on the rest of the PC. You can find a perfectly fine graphics card that is one or two generations old, that will run pretty much any game made today at full resolution. In the future, when games are released that require even more GPU power, you can always upgrade the graphics card, or add another one, if you have an SLI motherboard.
Those are some common mistakes that a first time builder will make trying to make a "budget gaming system". The same thing happens with cars. Guys will spend a crap-load of money tricking out their car with the latest aerodynamics, ground effects, spoilers, high end wheels and race car tires, yet leave their engine stock. What a waste of money. What good are race car tiers when your car won't go over 90 miles per hour? Same thing applies to a computer. There is no sense in over-building one particular part of the computer, when the rest of the computer won't let the higher end part run at full speed. You need a balance of power in the components. Don't strap a rocket engine to a skateboard.
Here is where you should spend the money:
1. Get a decent power supply. Cheap-o power supplies can fry your motherboard, cause mysterious crashes, have bad voltage regulation, and might fail in a year or two. Get a decent power supply up front, but don't go overboard with the wattage rating. You don't need a power supply big enough to power Las Vegas if you are building a budget gaming rig. Stick with something around 500 to 600 watts. Also, don't get one with modular connections. They are a luxury. You will pay extra for that luxury, and once the side of the computer case is buttoned up and your PC is turned on, you get no benefit from those modular cables whatsoever. It makes wire routing a bit easier, but you can install the DVD drive one spot lower in the case and hide all the extra power supply cables in the area on top of the drive, safely tucked away. I prefer Antec power supplies. They never seem to break, not on any of my dozen or so computers I've built in the past 15 to 20 years.
2. Get decent name-brand motherboard. Don't bother getting a board with USB 3.0 or SATA 6 Gb, as there are very few devices that can take advantage of either standard yet. There are no budget hard drives that can max out a standard SATA 3 Gb connection, so the bottleneck is the speed of the drive itself, not the connection on the motherboard. I prefer Asus or Gigabyte boards, but thats just from my own experience in the past. Its your choice to go with a full ATX or Micro ATX, the difference is in how many ram slots and expansion slots there are. If you are really strapped for cash, you can save a lot by going with a Micro ATX board, just make sure it has at least one PCIx-16 on it. If you get a Micro ATX board, you should still get a regular mid tower ATX case, so you can install full height cards, not low profile cards.
3. Get a decent size monitor. 22 inches at minimum. Pick one with at least full 1080p resolution (1920 x 1080) and is "HDCP ready", that way you will be able to use to watch High Def videos from any source, not just your PC.Settle on a monitor AFTER you pick the video card. Make sure the monitor has an input that matches what is on the video card (VGA / DVI / HDMI / Display Port). Make sure it has at least one HDMI port if you want to use it in the future with other high def home theater equipment.