Commonly used crimp sizes include:
6.3mm / .250" - Not used too often, but some microswitches have straight .250" tabs and some use a stepped design (shown) that can work with .187" or .250" if you seat it fully.

4.8mm / .187" - The most common size for American/European sticks/buttons.
2.8mm / .110" - Mostly used on older leaf switches/joysticks and Japanese buttons.
Which connector size do I need? I'll be using Happ Push Buttons and Happ 8-Way Competition Joysticks.
Normally my snap answer would be .187", but I got a batch of Happ buttons from Andy a while back that had .250" straight tabs. (Used them for the build in my sig)
Next button (+ Mini-Pac w. 4.8mm harness) order from Andy had stepped side .187"/.250" tabs.

*Bonus question 1: Does an 8-way joystick use up 8 inputs on the Mini-Pac?
Nope, only 4. You get 8-way by closing 2 switches at once. (Up+Right, etc.)
**Bonus question 2: If I were to buy illuminated buttons, what size connectors do I need?

For this type, use .250" for the two downward-pointing LED connections and .187" for the microswitch.
Scott