1. Yes, both Blu-ray players and HD DVD players will play regular DVDs.
2. Upconverting DVD players are still DVD players and as such, will play DVDs. The terminology of "upconverting" just refers to the player scaling the picture up to 720p, 1080i, and/or 1080p. Note that this does not mean that it magically transforms the picture into high definition; it just does its best to make it look like HD.
What should you get? That's up to you. If you want to take a chance on high definition on disc, there are several Blu-ray players or HD DVD players, and a couple combo players. Bear in mind that one of the formats -- or even both -- could conceivably disappear and you'll be left with media that won't play on future players. BUT you'd be enjoying hi-def on disc now.
If you prefer to wait it out, like me, just get yourself a good upconverting DVD player and you can't go wrong. If you get starved for hi-def movies, hey -- there's always hi-def broadcasts.
cheers,
supervij