This is probably overkill for your purposes, but I beleive this represents the best box in the sub-300 range. Might be a stretch, would take some work. All prices are including shipping. Some of this you can cut down on, but this is what I would do if building a budget HTPC:
1. Refurb Biostar M7NCG 400 nForce2 IGP mobo @ newegg - $20
-These come up at least a couple times a week at night, stock goes fast (usually a couple minutes at max) although it's doable, I snagged one tonight
-Integrated video, audio, network, and tv output (would need to build a convertor for the tv, cost is basically nil)
2. Used 1700+ TbredB and heatsink w/some light overclocking - $35ish
-These aren't hard to find if you watch the major fs/ft forums, and most do 2.0 easily with little or no voltage increase.
3. Infineon 6A or 6B chips DDR, 256mb should cost around $25 on ebay
-Will do 200mhz 7-3-3-2.5 @ default voltage. 512mb is a bit more than you need, 384mb should be perfect. Buy one stick to start but add another as needed for dual channel.
4.. ATI E-Home wonder TV Tuner refurb @ newegg - $48
-This also comes up rather often, at least a couple times a week. This is the best hardware encoding card you're going to find for the price, with the hauppauge PVR-150 coming in at around $70 but having a bit better software compatibility.
5. Case - Anything you want, I would say go for the $40 Powmax micro atx desktop case @ newegg. Not elegant, but it's cheap and gets the job done plus it has a power supply. Remember that if you plan on using a full sized video card later, its well worth getting a case that supports them. Pretty much all the cheap desktop cases are half height.
6. Keyboard/Mouse - Lite-on Airboard $23 @ newegg.
-Awesome for HTPC's, has a built in mouse that is fairly good but it does take a couple days to adjust to. I'm using mine for web browsing and its almost natural to me.
7. DVD Drive - Toshiba SDM1912-TA - $25
-Not the cheapest dvd-rom drive but super quiet and reliable. I would recommend toshiba over all others, especially lite-on (which is an excellent value but almost all of them are noisy)
8. Hard drive - Samsung 80gb 7200rpm for $62 @ newegg.
-You can do cheaper with used or old, I wouldn't go under 80gb.
9. Remote - Anything will work, depends on your needs. For a pure budget system I would just use the airboard.
That comes up to $278, but you're getting one kickass box for that. I didn't include any software prices since that all depends on personal ethics and/or needs.