Galaxy S3 Mini - my provider only offers micro and nano SIM cards I've ordered a [Samsung Galaxy S3 Mini] (hasn't arrived yet) :

http://www.gsmarena.com/samsung_i8190_galaxy_s_iii_mini-5033.php

On the above link, it says that it uses "Mini-SIM". 

I've tried double-checking that info on Samsung's site, but there it only sais "Sim Support":

http://www.samsung.com/uk/consumer/mobile-devices/smartphones/android/GT-I8190RWABTU-spec

My problem is, my provider only lets me switch my standard SIM to Micro-SIM or Nano-SIM.

Is there a way to make any of these work with the Galaxy S3 Mini? Anyone who already owns such a phone has had this issue? (and hopefully solved it)?
A Mini-SIM is the same thing as a standard SIM nowadays. The term was coined back in the day when SIM cards were the size of a credit card. Thus, the current-day regular SIM was known as Mini-SIM. Micro-SIM is the next step (used in newer smartphones, examples from GSMArena) and then there is the Nano-SIM (used only in iPhone 5, iPad mini and Asus PadFone Infinity, as far as I know).

See GSM SIM card evolution for graphical representation.