Not so much concerned about downrange energy or anything. Just want to punch holes in paper at 200yds.

Obviously, calibers other than .22LR are going to be more expensive. That's OK if they're substantially better at 200yds:

.17 HM2
.17 HMR
.22 LR
.22 WMRF

In summary, what would be the least-expensive choice that still gives good performance.

Mike