I will try and answer your questions more directly here...
In general yes, your work can be reproduced from a 2D design. The challenge comes if you are trying to recreate something with critical dimensions - like a piece that needs to fit in to another. If its a piece that you can have more creative liberties with, and sizing does not have to be perfect, its less problematic working from a 2D starting point.
In short- pick a designer who has done similar works to your project. There are some major classes of design so just find some alignment there - If you are looking to model a character or person - you will want to find a designer who specializes in that type of thing (and that's not me). If it is a complex precise design you might look for someone who does parametric design. If its a more organic shape such as jewelry, or a product prototype you probably want a NURBS based design, and pick a designer familiar with those types of designs and toolset.
The second consideration is that your designer is familiar with 3D printing processes and materials, and the design implications. They should know what will work and what will not, and be able to tell you from experience how to adapt before you pay for a useless print.
There are two files that are important. The native design file type (determined by the tool it is built in) and the 3D printing definition file - in most ases you will want is an STL file - that is what you will submit to your 3D printer. If you want flexibility to modify your design in the future you might require it built in a specific product that you desire. The thing to be careful is having someone build it in a consumer tool - as it may not be very portable to other design tools if you wanted to do something with it in the future. If this is a one shot thing, you just want designed and printed, your only requirement could be getting the STL.
If its a simple design it might qualify for a $40 flat fee design. If its an dynamic/organic shape, complex, or precise then the hours will go up. A "typical" design of a small object with moderate detail should take between 1-3 hours. Rates vary from free (people will do it because they want to learn the tools) to over $100/hour for larger professional shops.
Happy to bid your design project if you would like to send me the picture.
Sam Fleming
http://www.thelostpiece.com