Choosing a PCB Manufacturer/Assembler for the first time
Depending on how time-critical this is, go to China. There are loads of Chinese places that will do this for a much better price than anywhere else. The only drawback is it takes more time. 
I have personally used iTead and fusion and have had no problems whatsoever with their finishing. The only issue I had was if the silk screen is too small, it gets a bit illegible, but that has only ever happened when doing a space critical PCB with 0402 components.

It is up to you to do the math for if it is worth doing the soldering yourself or not. For something that sounds quite simple with few components, and only 50, it may be worth doing it yourself, and if you do larger batches in the future, then look at getting somewhere else to do it for you.

As for what you should ask them, ask how much it is for different size batches (some do 'price per PCB' reductions every 50, some every 100 etc) and ask them what quality checks they do, and what process controls they have in place to avoid problems. Ask minimum drill size, for vias, trace to trace width etc.
You will have to ask them how much it is to source components, they should be able to give you a quote on that, and then you can check yourself to see if you can get it cheaper.

It is up to you whether you want to go local for speed of delivery, or afar if you can wait, but do expect quite a price difference if you decide to keep it local!

EDIT Both of the places I recommended also do very cheap prototyping, usually in small batches (10) where you can verify your design. For prototyping, it is most likely worth assembling yourself so you can do anything you want to do during assembly to help testing.