For a server, you just don't need that much horse power. If you have a MicroCenter in your area, they have some serious loss leaders going on with the CPU right now. $99 gets you an Athlon II X4 635. That is 2.9ghz stock, with retail heat sink. I've got one of these running as an ESXi server, which is hosting virtual machines running an Oracle database, WLS, WCI, UCM, and a few other bits.
http://viewer.zmags.com/publication/5ca709e7#/5ca709e7/2
They also have a deal where they will give you a free motherboard with a CPU, or $40+ off a more premium board. After everything is said and done with the bundles, you are looking at $30 for the mainboard if you pick it up with the CPU.
http://viewer.zmags.com/publication/5ca709e7#/5ca709e7/4
I've got the GA-MA785GM-US2H AM2+ 758G mATX Motherboard ($30 above). It has 4 DDR2 slots, which can handle 4x4G configuration. I picked the DDR2 based board over the DDR3 based variant, as I had 8G of DDR2 RAM already. Performance at stock speeds won't make much of a difference at this point. DDR2 RAM is slightly cheaper than DDR3 - but it would be a toss up. The board also has built in video - integrated ATI Radeon HD 4200 (DX10.1) - which is more than adequate for a server configuration.
Find a fast traditional HDD. You don't need a lot of storage, as this is a server. I think I paid $75 for a 1TB 7200RPM Seagate. A bit more performance with the WD black models - the new 1TB WD black
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136533
is a very nice performing HDD at the $100 price point. Large cache. Since you will be doing a fair bit of writing to the disk, I would avoid the solid state drives for the server. No bang for your buck at this point.
I would add in 4G of RAM, at a minimum. Does not need to be overclocking grade stuff. DDR2 800 is more than adequate. I would try to get sticks that are closer to 1.8v rather than 2.0v, just to keep heat/power requirements lower. Something like this, for $86 shipped. There is absolutely no need for ECC RAM in a TF2 server. I don't bother with it on my development workstations or the VMWare servers that are non production. Production hardware, where money per second lost... that is a different class of hardware.
http://www.newegg.com/Product/Product.aspx?Item=N82E16820104001
And that gives you room to bump to 8G is you need to later. If this is a dedicated server, you won't need more RAM - assuming you can keep your hands off it for other uses at the same time. (grin)
You don't need much of a power supply to run this. My server is chugging along with a 500W PS. The CPU is ~95W and the rest of the hardware should draw less than 200W. Spend money for a quiet 500W PS. You could use a 400W if you have one laying around. The above motherboard needs the 8-pin ATX, which might be an issue if the old PS is too old...
If you act before the end of this month, there is a combo deal for the PS/HDD
http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.413537
The 750W ps is way overkill for what you need. The 500G 7200 HDD is also large enough for the dedicated server - 20G should be overkill. Shipped, after rebate for $75. Not a bad deal, assuming you are starting from scratch.
(older calculator here -
http://extreme.outervision.com/PSUEngine The CPU is not listed, but the x4 940 is a reasonable substitute )
No need to buy a DVD-ROM for the computer. Use a CD-ROM from an existing box for the OS install, then remove it.
A cheap, razor sharp interior, chassis can be found for $20 or so - look for 'free' with rebate deals. Short term, you can just use the cardboard box the motherboard came in, with a few holes in the side.

(
http://heelix.multiply.com/journal/item/91/Pizza_box_computer.)
So hardware, were I doing this from scratch.
$99 AMD X4 935 CPU w/heatsink
$30 Gigabyte GA-MA785GM-US2H mainboard
$86 Kingston HyperX 4GB (2 x 2GB) 240-Pin DDR2 SDRAM DDR2 800
$75 Thermaltake 750W ATX, Seagate Barracuda 7200.12 500GB 7200 combo
$20 for cheap chassis
Should be just over $300.
For the OS, you would be silly to not do Linux. Never mind the money part, you will get far better performance running a bare bones router style install of Linux. Windows nurfed the TCP/IP stack on the consumer versions of the OS. I'm personally partial to Centos, which is the open source version of Red Hat Enterprise Edition. You could also do Ubuntu, but you should be doing a minimal OS install - not even XWindows - which I find easier on the Centos side.
http://centos.org
A couple very good starting points, btw:
http://www.nsa.gov/ia/_files/factsheets/rhel5-pamphlet-i731.pdf
http://www.nsa.gov/ia/_files/factsheets/rhel5-pamphlet-i731.pdf