The 17 HMR is loads of fun to shoot. It shoots flat enough that you can practice out to 300 yards and still maintain a decent level of accuracy, plus it'll kill varmints at distances previously left to the 22 Hornet and other small caliber centerfires. It is more expensive to shoot than a 22 lr but still lots cheaper to shoot than centerfire ammo. I like practicing with the rimfires because it is quieter, cheaper, and lots of fun.
That being said, there is something to be said about practicing with guns that recoil too so that you're comfortable with it and know what to expect.
I personally shoot a 22lr, 17 HMR, and 22 WMR the most in the spring to work on basic fundamentals like breathing and trigger control. It gets me ready for rock chucks on the outskirts of town that can't really be shot with centerfires due to neighbors complaining about the noise.
I also practice a lot with a 22-250 in the late spring/early summer that helps me get used to a louder gun (noise honestly causes lots of flinching in many people). About July I pick up the 300 WSM
and practice with it more frequently to get ready for the big game season in October.
I use all my guns year round, but I do have phases throughout the year where I shoot one gun more than the others to get ready for specific hunts.