Sophia already answered the main point quite well, but I thought I'd chime in with a little more detail for you:
From: Lepton Leandros
I have a prim face, lets call it 512x256, and I want to put a texture on it, and several questions have come up.
It looks like only TGA, JPG, and BMP textures are allowed. In my case, my texture is mostly some text labels, only on the bottom quarter of the face, and the whole rest of the face can be a solid color. So since there is text involved, even though it is a fairly large font, JPG is probably out. But TGS and BMP seems like it would be huge. GIF or PNG would be great for this type of texture..
As Sophia said, SL's internal format is jpeg2000, so the source file size is pretty much irrelevant. You should avoid jpeg altogether, not just because it can fuzz text, but because it's a low-quality format (which of course is why it blurs your text in the first place). Once you upload that low-quality compressed image to SL, it will be re-compressed into jpeg2000, and it will lose quality even further. TGA is always the way to go, 24-bit if you don't need transparency, 32-bit if you do.
From: Lepton Leandros
When you make a TGA of 512 by 256, at 16 bits/pixel, that's a 256K file, no matter what the texture is, even a solid color. I'm using Adobe Illustrator to export to TGA and I don't see a compression option.
The reason you don't see a compression option is because TGA is an uncompressed format. Were you to compress it, it would no longer be a TGA. Also, I know this really isn't the question, but just for clarity sake, don't use 16-bit. For SL you want to stick to 8 bits per channel, meaning 24 bits for RGB or 32 bits for RGBA.
From: Lepton Leandros
1) Is this how SL stores the texture, 256K uncompressed? Ouch!
As has already been said, SL compresses everything to jpeg2000. You're right that it would be a big "ouch" were files to remain uncompressed. Every 512x512 image would be 768K or 1MB, which would pretty much make operation over the internet in real time impossible, and would eat video cards for lunch. Thank the pixel gods for jpeg2000. It's such a great format.
From: Lepton Leandros
2) On a texture with mostly text on a plain background, what's the best format for uploading?
Again, stick with TGA. Technically you could get away with BMP, but it's a good habit to stick with TGA at all times. TGA is the most common format used in 3D graphics.
From: Lepton Leandros
3) In my case I really only need the texture on the bottom 512 by 64, is there some way to apply this to the 512 by 256 face? I guess not.
I'm not sure what you mean by "the 512 x 256 face." If you want to put a 512x64 pixel texture on just one face you certainly can do that, or you can just offset a larger 512x256 so that only a 512x64 section of it is visible. To do the latter, just set the repeats per face to 0.125 in whichever direction the 64 should be (I'm assuming vertical) and to 1.0 in the other direction.
From: Lepton Leandros
4) In my case I could use a texture with transparency - put the text on a transparent background, and give the face a solid background color. But with transparency at 32 bits/pixel, this seems like an even worse option. What's a good way to handle this? If SL compresses textures internally, this might actually be a good option, since transparent and solid areas should compress very well.
If you put the text on a transparent background, the only way to get a solid color behind it will be either to hollow the prim and make sure the inside is not transparent, or else to put another non-transparent prim behind it. It's not a good idea to use transparency unless you really need it. SL, like many graphics applications has issues with alpha sorting. Put two 32-bit textures near eachother, and they fight for screen dominance all day long. Stick with 24-bit unless you actually do need to be able to see through something.
You're right about the compression part, in that solid areas of color and/or transparency do compress smaller than areas of high contrast, but I wouldn't let that dictate your texture-making decisions. SL is pretty good at displaying textures quickly, as long as the canvas size is not huge. Don't sacrifice image complexity just to get a little bit better compression rate. Good artwork is always worth a little extra file size. Just keep it 512x512 or smaller, and you'll always be fine.