OK... I used to run a print shop so i think i qualify to answer this.
Any print shop that can print 36x20 inhouse will be using a large format inkjet printer, id say Epson, HP or Canon.
Assuming the printer is reasonably new (IE < 4 years) it will almost definitely use good inks - in Epson's case UltraChrome. IF the print shop uses a constant feed ink system (after-market) personally id steer clear as they could well be cheap crap inks off ebay which will fade in weeks.
Note: you wont get a choice of ink - you will get what they use!
A GOOD printer will accept nearly any format, but for photographs we prefer TIFF, or 100% quality JPG.
If they are any good at what they do they will have a dedicated computer for their print system (s) and they will have a fully calibrated monitor. get them to show you the image on their screen - BECAUSE they will have calibrated their complete work-process in such a way that the image on screen looks very close to the printer output - so if there is a green cast because your monitor was a bit off, then that is how it will come out.
Yes most good printers will check the image for you before printing and highlight any issues, most will be happy to do minor tweaks to colours but will get you to view/sign off the changes before print.
I would go with gloss or semi-gloss / lustre paper if its available and get 250GSM+
However you will pay for a good service like this - i would probably charge ITRO £40 for a full quality print of that size on good quality media (Kodak / Epson) with archival inks (UltraChrome K3)
If you want to pay £5, then expect "a print" !