Some HDTV is progressive scan. HDTV formats are 720p, 1080i, and 1080p, although no one seems to have produced anything that is 1080p. In those designations, the "p" stands for "progressive" versus "i" for "interlaced."
If you buy an HDTV monitor, you should look at what formats it is capable of displaying. Many will display 1080i, 720p, and 480p (DVD std). Because you have an HDTV does not mean that you do not want a progressive scan DVD player--just because the set will reproduce 1080i or 720p does not mean it will upconvert a 480p or 480i signal to HDTV for viewing. I can't think of any that do.
Component video is analog. DVI is digital. If you get a TV with DVI, make sure its HDCP compatible, or when they start showing stuff with encryption, you won't be able to watch it.
To my knowledge, you can't convert a VGA to component video. There are some HDTV monitors that are capable of displaying VGA signals. Many of these use the component video inputs, but its not converting a VGA signal to component video.
A line doubler is not the same as progressive scan. A line doubler does exactly that--it doubles the number of lines of resolution by interpolation, but it does not inherently modify an interlaced signal and convert it to progressive. Many may do that in the same box, however.