Some considerations: ( I am helping my daughter right now address this same possible conversion) I suggested that she get input from a real estate broker about whether this hurts the resale value of the house. They have another tub, and plan to be in the house for a long time, so this will probably not weigh high on their list, but think about it, anyway.
As t the plumbing, the tub is on a 1½" drain, and the shower must be 2" . Probably, the 1½" trap below the tub connects to a 2" branch within a fairly short distance, so a plumber would need to see this to determine how easy or hard it will be to fix the drain. It this is on a slab, it might require a little "hard rock mining"!
The total cost for materials for a new shower valve, pan, or tile floor, and tile walls could be under $1000. If you want a corian pan, or corian or slate walls, this would be higher. The shower valve could run from $100 to $500 or more. When you start looking, ask some questions here, because we have lots of opinions on that subject.
The labor to do this is a lot, so if you contract it done it will be expensive. Can't even guess on rates in your area, and not seeing the job.
This type of work is a challenging but very doable DIY project if you are so inclined. You can get plenty of plumbing info right here, and if you want to get into ceramic tile, just get some book, take a class at the homestore, and especially cruise over to this excellent tile forum:
www.johnbridge.com
The homestore will help you with the actual tile install info, but may be very light on how to properly prepare so that the walls are plumb and waterproof. That's where these forums come in!