There are two main ways to go about this. 1) Get a TV Tuner card for your computer and tune the tv channels through that. This can be done using any monitor as long as your computer can display its screen on it.
2) Buy a TV that has both a VGA/DVI input for the computer and contains a TV tuner so that you can use it as a normal TV.
The first option will be definitely cheaper, you can get relatively inexpensive tuners (<$100). The main point is whether you want a big computer screen (which might be slightly expensive) or you just want to use a regular one. eg) My Dell 17" has a resolution of 1280x1024. This is pretty high and works great as normal TV reception and perfectly as a computer screen.
The second option is slightly problematic. Not only will getting a TV be expensive, it will also have a lower resolution for it's size as compared to a simple computer LCD display. Then there's also the fact that if you want a nice 30" TV, you'd need to increase the viewing distance from your screen dramatically as you won't be able to sit too close to it. This coupled with the lower resolution per area and the price means this really isn't the best option if you intend to use your computer a lot as well as the TV.
At this point I wouldn't worry about HD signals. I don't think you'd be able to receive many (if any) over the air HD signals for free. If you want you can pay for it but then this costs money (and you'd need a cable box, etc). Not only that buy you'd receive relatively few HD channels because there won't be many to begin with.
Whilst drifting suggested getting a 1080p screen, again I wouldn't worry much about it. Especially at lower screen sizes (30-40 inches) you'd be hard-pressed to find a 1080p set to begin with. Even if you do, it will be expensive, and at screens that size you won't notice a difference. 1080p is really only distinguishable at 50+ inches, at which you'd really be incapable of using it as a computer screen.
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