Honestly, I'd go with the PSP for the FF Tactics remake alone. All of the same great gameplay, some new classes and sidequests, and a much better translation of the already awesome story. It beats anything on the DS that you haven't already played in some other form if you ask me, and you'll get plenty of playtime out of it. I believe it took me more than 50 hours when I played it originally on the PSX, and I'm about 10 hours into War of the Lions right now. Definitely an amazing game that you shouldn't pass up.

With respect to your first and second questions; FFIV Advance is a port of the original hard type FFIV game with a vastly improved translation over the initial SNES release and two secret dungeons, and FFVI Advance is pretty much the same deal as FFIV Advance, new translation, two new dungeons and a couple of new Espers. It was certainly an improvement, but I wouldn't say it's worth purchasing a DS for by itself.