Ah if you had asked this earlier I could've given you a precise answer! Have a booklet filled with all kinds of paper and even weight and gloss.
I would first check reviews from friends and online to see where and which one the best nearby copyshop is because not every copyshop is equally good. Took me 3 years to finally find a great one. Cheap and fast doesn't mean cheap quality.
Ask the workers there for a test print and what they'd recommend for your kind of work and its purpose. And I wouldn't order prints online at first.
Keep the print as .psd .jpeg or .png and also .pdf and ask them which they prefer, probably pdf. 300dpi makes them and you happy.