I'm more interested in quick response than price (to a point obviously), and I don't mind having to get three copies of a board. However, I would like to be able to send Eagle files rather than learn a new program (especially if it only runs on Windows).
You don't need to learn a new program - just use the post processing (cam) jobs from Eagle to generate Gerber files.
The only place that I know off, where you can get PCB's made from Eagle files is Olimex
in Bulgaria. If you're willing to pay for delivery by courier, it usually takes from 3-5 days of processing time plus 1-3 days for the courier transport - is that fast enough?
(I don't think you'd get it any faster if you used a local manufacturer - au contraire).
This is, if you stay with 10 mil or wider. If you need to go to 8 mil, add a couple of weeks.
Get the Eagle scripts from their site to check the PCB and try to keep through holes to a minimum number of different sizes, for the lowest cost.
The quality of the PCB's from Olimex is very good.
Unless you're an experienced PCB designer ace, it may be a good idea to post your PCB files here for tips and advice before ordering a PCB from them, as there are many pitfalls.
Of the many PCB designs I have seen (here and on other hobbyist sites), I have not seen a single that couldn't be improved in some way and most of what I've seen really needs
to be improved. It's annoying to find the weak spots after you paid for the manufacture.
Did you consider making PCB's yourself?