First, the word, "has to be done soon" is alarming. You need to find a reputable contractor and busy contractors are generally the better ones and one that can do it tomorrow, is not busy, wonder why?
be patient, get several bids and ideas and do not be in a rush.
First, you need to decide if you want a seamless one piece, fiberglass contained shower stall, or one with ceramic tile.
I would shop around at the home center. Pay attention to the contained units. They will not leak and will stand up for a long time. You just have to find one that will align with your existing drain pipe.
Building a ceramic stall entails installing hardi board, installing ceramic tile and grouting.
You are looking at material and labor in the area of $2 to 3000.