What type of machine do you use?
There are lots of longarm machines on the market.  Some of the most widely known are Gammill, APQS, A-1, and Nolting.  Be wary of the quilter who used a small home machine or one that is not industrial.  I don't mean to eliminate that person from your short list, just be aware that if the quilter is using a home model of machine, she/he probably isn't in the business for the longrun.

Is there anywhere I can see your stitching?
If the quilter has a website, she/he probably has pictures posted, or if she is local drop by to see some quilts she is currently working on. 

What is the turnaround time?
This would be the amount of time between when you commit to sending your quilt and the quilt returns to you.  Some longarmers have a shorter turnaround time than others.  The turnaround time varies with how many quilts are on hand and how fast the quilter can quilt them.  A short turnaround time is not necessarily a good thing.  You don't want someone in a hurry working on your quilt.  A unreasonably long time is not a good thing either, as you will have to wait so long to get it back.

When (how far in advance) should I send my quilt to you?
The quilter you choose may not want you to send your quilt until a week or so before she/he is ready for it. 

Where can I see what patterns you offer?
Most have websites for you to view what they offer in patterns.

Do you offer custom quilting as well as overall designs?
This is important if you really want something specially designed for your quilt.  Someone who specialized in overall patterns would not be the one you want to hire to quilt your heirloom.

Do you offer freehand quilting designs as well as pantographs for overall?
Some quilters will do overall freehand designs that compliment the piecing or theme of the quilt.

What types of threads do you like best?
Not only is there the choice of solid or variegated, but does she/he use any specialty threads like the very beautiful tri-lobals?

Do I have a choice in the color of thread that will be used?
If the quilter you are speaking to will not let you choose the thread used, then go on to the next quilter on the list.  Granted, some quilter will not use a particular thread just because it does not run well in their machine.  If this is the case but you feel very comfortable with this person, just choose another thread.

Do you charge for extra services?  (ie: binding)
Most will charge for extras like binding, backing, batting.  Beware of the ones who promise a completed quilt for a very low price with all these extras included.  They have to make up the short fall somehow or go out of business.  You most likely will be getting inferior batting, fabrics, workmanship.  The exception may be the quilter who is trying to get a business started and grow a customer base. 

Do you have batting and backing on hand?  If so, what choices/prices?
Most will have at least a few choices here.

How long have you been using your longarm machine?
Very important question.  The longer she/he has been using the machine, the more comfortable they are and the better the stitching.

Do you do the quilting yourself, or do you have someone else who works for you do it?
Another very important question.  Many commercial shops have employees doing the quilting.  This isn't necessarily a bad thing, but it is something you want to know before sending your quilt.  You may want to ask to see some of the employee's work.