All of the boards we've produced over the last several years have been done with
FreePCB. To be honest I don't have a lot of experience with other packages - I've tried Eagle but never quite got used to it, messed around with KiCAD a bit, etc. but I always end up back at FreePCB. (I never got to the point where I felt the need to buy a commercial package - our projects are small and there's enough free software out there to get the job done). As an added bonus, the author is apparently involved in FIRST.
For board manufacturing, I've used
www.apcircuits.com,
www.pcbfabexpress.com,
www.batchpcb.com, and ordered full panels from
www.goldphoenixpcb.biz. That last one is a board house in China (it's the same one used by
www.batchpcb.com), but you'll have your boards in 7-10 days after ordering. You'll get a lot of boards because they make a whole panel, but often the cost of the full panel from them is about the same as getting a few prototypes made at the other places. I've had very good results from all of these places - the differences are mainly in pricing versus leadtime. APCircuits is great if you need the boards fast - if you don't need soldermasks they'll ship the next day for a reasonable cost. PCBFabExpress is what I used when I needed a small quantity (2-4) boards with soldermask with a short turnaround time. BatchPCB is excellent if you're not under a time crunch (order to delivery can be 4+ weeks), and GoldPhoenix is what I've used whenever I know I'll need more than just a couple boards because the cost difference is low. Also, be advised that GoldPhoenix sometimes runs specials on eBay.
There's a (somewhat lousy) picture of one of the boards we did last year in
this post. We designed those with FreePCB and had them made at Gold Phoenix (along with our custom circuit board that was used on the robot).