Moving a joystick is fundamentally different to moving a mouse. With a joystick there is a spring constantly acting to center it - no equivalent force when using a mouse. So you need to get a feel for estimating that force and accurately counteracting it in various gameplay scenarios. That's a completely different "muscle" to have a memory of vs. using a mouse I think

Also, modern controller joysticks generally are not great. Most have medium to large deadzones in the center by default. I'd recommend reducing them for more responsiveness. It comes with the tradeoff of being more susceptible to stick drift. But that isn't something you should be afraid of. It's a physical impossibility for their design to not wear over time. I'd recommend recalibrating and adjusting settings regularly. At the end of the day, replacing joystick modules only requires screws (no soldering) so it's cheap and relatively easy.

If you're really serious you could get some hall effect joystick modules. That way you wouldn't need to recalibrate often and could keep a consistently small deadzone setting without encountering drift. i.e. default settings from like dualshock 2, when stick drift was just as apparent but people hadn't gone crazy over it yet.

Minecraft would be fine for learning fps movement in a relaxed setting.