We are in the beginning process of remodeling our small family bathroom. We
are swiching out the cabinet style sink w/ a pedestal, putting in a new one
piece toilet and ripping out the old floor (Including sub floor).
Right now I'm trying to figure out what to do w/ the bathtub/shower.
Structurally the tub is sound, however it's about 60 years old. It's
chipped and dirty no matter how much I clean it. There are flat white
ceramic tile in the surround that are in good shape but for the mold issues
in the grout.
My choices seem to be:
leave the tub and surround as is (the worst choice)
Have Rebath or something like that, come in and put a new coating over the
surround and the tub.
Having a new tub and surround installed (from a kit)
New tub and ceramic tile (but I'm worried about mold in the grout again)

I really have no idea what the best thing to do would be. We are trying to
do this as economically as we can.
Any thoughts or ideas?

The right way to di it is to replace the tub. The paints don't last
very long. A few years if you are lucky.