Depending on the ranges you want to shoot and at what, you could get by with just one barrel, or want several barrels. Easy and cheapest answer if you want to stay with what you already shoot is to get an Encore rather than G2 frame as it will handle all of them safely. Adds about a pound to the action weight as well, but you still will probably not see hits with the 22-250 or 243. If you do want to stay with a G2 (or as I have with Classic Contender frames), the lower end is covered but a lot depends on if you are willing to do wildcats to match or exceed the 22-250 or 243. Easily done with the wildcats available that are safe for the smaller frame, and there are many choices. But they come at a price of custom or rechambered barrels, often expensive die sets and more brass prep and forming work.
I live in the west where both predators and varmints have been my mainstay for many decades. And they are shot often with Contender pistols and carbines. The possibilities are almost endless with cartridge choices, but certain ones do become favorites depending on what the target is, how far away it is and how high the winds are. Some of them will do double duty, others are more specialized. So it really just comes down to how much money you want to spend.
It's hard for me to go to the digger fields without a 17M2, 17HMR, 17 Ackley Hornet, 17 Remington (or equal wildcat) and 24, 25 or 26 caliber wildcats. Covers all you can see as far away as you can see them. On digger shoots I often take a dozen to dozen and a half choices along. The 17's give you choices that will cover anything you can do with your 223 down and the wildcats will exceed what the 22-250 and 243 will do.
For predators it's hard to beat a 17 Rem (or 204 Ruger) or any of the wildcats that match them ballistically unless the ranges get longer. When they do the 24, 25, and 26 wildcats take up the slack.
On a duel P&V hunt I just have to have a 17 rimfire along, a 17 Ackley Hornet for the most fun wildcat there is, a 17 Rem or one of my wildcats that approximates it and one of the 24, 25 or 26 wildcats for when the ranges get long and winds high. So I guess my minimum would be 4 barrels even though I could easily get by with one if I had to and just limit my shots.
If you don't want to dive into wildcats at all with a G2, I'd probably opt out for choices like a 17 rimfire, 22 Hornet, a 17 or 221 Fireball, a 17 Rem or 204/222/223 and maybe a 7-30 Waters for the longer, windy shots.
If you decide you do want to dwell in the smaller frame wildcats, I've done most of them over the years and can offer some insight on them. Just drop me a PM with what might interest you for suggestions.