what do i need to write DVDs?

Ok, so I'm looking for advice on what sort of computer equipment I need for
the project I'm taking on. I work at a talent agency and we want to be able
to put together our actors' demo reels on DVD. Up to now, we have been using
video tape. For a bunch of different reasons that are pretty obvious, it
would be better to have them on DVD. Generally, the reels will only be 10-15
minutes in length. We need the DVDs we make to be playable on standard DVD
players, not just DVD-ROMs or whatever. We also need to be able to extract
scenes from other DVDs and then save them permanently to the hard drive so
that whenever we need to cut a new reel, we can do it relatively easily.

So given what we want to do, what kind equipment and software do we need?
I'm thinking we may just buy a new computer specifically for this task. I've
been given a budget of $4K or so, but I was hoping to do it for far less.
Any recommendations would be much appreciated.