What range are you going to be shooting ? If 150 yds & under, the 22 Mag is cheaper with less noise so you can continue to shoot.
The undisputed King of Varmiters is the 22-250 which will really extend your reach. But there is nothing wrong w 223 as long as you get a 1:7 twist to stabilize the heavier 77 gr & up.
Mea Culpa, 1:7 is assuming you want the maximize range of 223 or are into long range shooting. On FTF it is best to never "assume" anything. Savage offers a tgt model w this twist. Most varmit rds for 223 are 55 gr or less and 1:12 Twist is optimum. There are compromises in the 1:8 or 1:9 range.
The round rarely mentioned is the .243 and it can double as a Deer rifle.