Assuming you're in a Cold Zone, not a Very Cold Zone, one inch XPS is sufficient. (For EPS, I'd put in two inches.) It just means you'll need a little more of whatever other insulation you are putting in between the studs. Same for metal framing. Just be sure the base is on 1" XPS; metal framing doesn't take kindly to water.

Worthy, if I install 2" board or 1.5", and then frame a 2x4 wall, do I need to install insulation (regular stuff) in the 2x4 cavity? Or does it get empty?

The link below are the recommendations of the US Department of Energy for cost effective installations.

(These may or may not exceed state or local requirements.)

In my location, I'd fill the stud spaces with fiber insulation, as R5-R10 boards fall below the required Code minimum.

Here is a link that might be useful: Cost Effective Insulation levels

https://www.energy.gov/sites/default/files/2014/01/f6/1_1a_ba_innov_basementinsulationsystems_011713.pdf This seem to be the updated link.