Should I build a HTPC? (Budget: ~$250)

Hello people of the Tom's Hardware forums! As you can tell by my title, I'm not sure about this potential build.

I live in the middle of nowhere (town of 200, less than one bar of cell signal, nearest sidewalk is half an hour away) and I've been suffering through satellite internet for the past two years. However, an internet company is finally bringing broadband up here. My whole family is psyched! My mom is in particular, because we can now get Netflix.

First off, for anyone with the knowledge, I'm trying to figure out how Netflix works. I know that you can have up to six devices on one account, however you can only use one device at a time. I don't know if you can download movies to watch later, or if you can stream the same movie to multiple devices at once. Any help would be appreciated!

Anyways, back to my question. We have an HDTV in our living room, but we only have a Wii, so we want a device that can stream in HD. You could probably guess by the fact that I'm posting here that I suggested building a HTPC for this. My mom didn't flat-out say no when I mentioned that it might cost as much as $300, so I think I can convince her that it's worth it. Below is the standard rubric for this build:

Approximate Purchase Date: Two weeks to a month from now, *if* I build this

Budget Range: About $250, preferably before rebates, but after works as well

System Usage from Most to Least Important: Standard HTPC (watching movies, streaming, Blu-Ray, etc.)

Parts Not Required: Monitor or speakers (using 55" HD CRT TV)

Preferred Website(s) for Parts: Newegg or Amazon preferably

Country: United States (in the Pacific Northwest)

Parts Preferences: Must be an HTPC case or other small, slim case

Overclocking: Probably not

SLI or Crossfire: No

Monitor Resolution: Unsure, definitely below 1920x1080

Additional Comments: Preferably on the quiet side, must include a Blu-Ray + DVD reader (writer not necessary). Read below.

I'm heading off to college in about a year, so I need a computer that my technologically-illiterate mother can A) Run without any problems whatsoever and B) Control entirely with a remote. Is this even possible? I don't have money for an OS, so I'll either be using Linux or a friend's spare copy of Windows XP.

Now, I have one question. Would I be better off getting some other device? Its only requirements is that it can stream in HD, can use Netflix, and preferably can play Blu-Ray. This is a completely new field for me, and I know absolutely nothing about HTPCs, so any help would be appreciated!

Tl;dr: Just read the last two paragraphs.

- Jak Atackka