I'm from the Netherlands, using Windows' Dutch US-International keyboard layout, where a fair few characters use dead keys (éèëê, times five for every vowel). On Windows, typing an apostrophe with a lowercase r puts 'r; however, typing the same sequence with the US-International keyboard with dead keys in Mint gives me ŕ. This happens for a lot of characters and it's quite annoying when you don't expect it. Is there a keyboard layout that behaves exactly like the Windows keyboard I'm used to? It could be either native or an installable package, I don't really mind.
What you're describing is known as a prefix input method. Most Linux IME's have support for these to some degree (I use one that works the opposite way, adding the accent after the letter it applies to, on a regular basis). I'm not sure what IME Linux Mint uses by default, but most of them provide support for an input method with a name like
latin-pre, which will behave in a manner similar to what you're used to coming from Windows, though it recognizes a lot of accent combinations that are not used in Dutch as well.
There are also keyboard layouts which behave similarly, but at least some of them instead require the use of a 'compose' key which indicates that the characters typed while it is held should be combined.