I have done tubs, shower surrounds, and a shower from scratch including preslope, liner, curb, all tile, etc.
I think the tub will be easiest among these choices. If you are going to live there a while, I would consider an insulated steel tub instead of fiberglass. Much more durable and not all that heavy; you can easily carry it with two people.
Getting it in: if your current bathroom has an alcove for the tub that's 5' wide, and the rest of the bathroom is wider, it won't be hard. Strip all old tile, sheet rock, whatever down to the bare studs where the tub will go. A sledge hammer, used with some restraint, works wonders. :-) Shut the water off, get the old valve set out, and cap the lines. Do you know what material your supply lines are yet? Galvanized, PVC, copper.. the first two are easy enough to replace a manifold without specialized skills or tools, but if it's copper, you may need to pay someone to braze the lines.
Assuming your framing and floor are in decent shape, get the new tub in place and roughly leveled. Then work on getting the new valves roughed in. Fasten the tub to the walls, install concrete board (Durock or similar; easily cut with a circular saw with a diamond blade). You'll probably need a masonry hole saw for where the valves go through.
The tile isn't hard; materials are cheap and you can do a few rows at a time. You can get a very basic wet tile saw for $50 at Harbor Freight that will work fine for moderately sized tiles. Use plain old mortar (no mastic); it's much more durable for wet applications but will require spacers and support for the bottom row. I usually use something like roofing nails shoved under each bottom row tile, then the regular tile spacers between rows.
Good luck! Here's my shower from last summer for possible inspiration. There are lots of photos of tile work in my house albums. :-)
Finished shower