You might be able to be a prefab enclosure that can go right over those tiles. If it were me, I'd just install new tile. You can use various sealers to keep the grout looking nice and clean.
check out Bathfitter,I had my 55 year old tub covered and it looks great,all done in one day
If you decide to retile, make sure the installer seals the new grout. Then, I would suggest an additional seal at six months, and then annually every year after that. This should keep your tile looking newer, longer, and prevent any seepage of moisture behind the tiles.
I will mention that the whole bathroom is tiled in an ugly green tile about chest height all around! I don't want to do a cover up of the old tub or tile, don't like the idea of covering up something that might be hiding underneath. I will retile, but else where.
I am pleased you don't want to cover the old stuff. There are practical reasons for gutting and starting over....but the concept of changing my clothes without taking a shower and putting on clean underwear doesn't sit well with me.... so I'm not a big fan of the half-a-dozen franchises that have popped up in the last few years that "cover the old".
There are some nice looking shower surrounds now available that were not a few short years ago. They aren't as nice as a custom tile shower, but it is all in what you want and can afford.
I am not an expert in the difference between the two, but acrylic is generally considered a higher end product than the old fiberglass. You can still purchase both types so get smart on it so you can make an informed decision. Tim
I will add that we just installed a prefab fiberglass about a year ago, and the look is MUCH different than the older styles... it was modern with curves, and built in shelves and a hand rail. (Small acrylic).
I have been trolling the big box online offerings as well as actually going in there. If I do that I do at least have another bathroom downstairs, but no tub there. I agree with Hewitt about not having the shower for a few weeks or so. Which is my dilema. I will figure something out and when would be the best time to do that.
We just put in a new tub had 60 tile everywhere. You need to take it just so you can put in cement board water resistant. Behind you old tile is probably just drywall. We put in a 4 piece sround. Very nice made Maxx.