Terms that you may find helpful:
e2e or edge to edge - this refers to a quilting pattern that repeats itself and runs from one edge of the quilt to another. This is accomplished either with a robotic, computerized system, or the quilter uses paper pantographs, manually steering the sewing machine and "tracing" the design printed on the paper with a stylus or laser. This is generally the most affordable type of quilting because it requires the least amount of work on the quilter's part.
b2b or border to border - very similar to e2e except the quilting pattern stops at the borders of the quilt. This gives the quilter the opportunity to quilt a different pattern in the borders. This type of quilting is usually computer-driven.
custom - This is the most expensive kind of quilting and typically is "steered" by hand. I know of a few quilters who will use robotics, but it's still expensive because the quilter has to design the quilt pattern specifically for the quilt in the software, and that can be time-consuming.
You will want to have an idea of how dense you want the quilting to be. A more dense pattern will take more time and use more thread, so the price may be higher.
You also will need to think about what you want the finished quilt to look and feel like. Do you want a soft, fluffy quilt that drapes around someone sitting on a couch? Choose polyester or wool batting and a less dense quilt pattern. Do you like thinner quilts, or maybe you want the quilting to shine? Choose a denser quilt pattern and a heavier thread.
Again - these are all things your quilter SHOULD discuss with you before you both agree on the job.
Ask for recommendations for longarmers around your LQS and guild members; learn what their experiences have been like. Ask to see quilts the longarmer has quilted. What's their turnaround time? A long turnaround time isn't necessarily bad, it might mean that longarmer is popular because she's very good. Or it could mean she's new and slow.