There are three types of groundhog rigs. I categorize them by distance a person plans too shoot.
Out to 150 yards- 22 Hornet
From 0 to 300 yards- 223 Remington(nothing heavier is necessary out to 300 yards).
From 0-600 yards- Any good caliber between .243 and .264(I like my 6.5X284). A 243 Winchester would also make a great choice for this distance.

The Handi-rifle will make for a fine GH rifle. If you are wanting too shoot past 300 yards then I believe you will have a problem with inexpensive optics. I also believe the Encore would be a better choice. I have a few different barrels for mine, and I really like it. Tom.