the 4:3 HDTVs are really HDTV, right? It's just that when they go to HDTV 16:9 mode, they blank the top and bottom instead blanking the sides in 4:3 mode, right?

Right.

And some of them have modes to compress anamorphic images vertically instead of stretching horizontally, right?

Right. Exactly.

It seems to me that a TV that can do 1080i must require better convergence than a regular NTSC TV. Is that true? Bad convergence has always been one of my pet peeves,

Heh, most people looking at tube TVs don't care about convergence. Us RPTV owners are very picky about it because it's adjustable on our sets. I remember making a joke on The Spot about "you know you've been tweaking too long when you start to notice convergence errors on tube televisions".

I would assume that a TV capable of 1080i would have tighter convergence than a regular TV, but I haven't actually done any comparisons. I don't know.

Do I need to make sure that the TV will support 480p, or is that a standard feature, or a standard HDTV feature?

It is a standard HDTV feature, not necessarily a standard TV feature.