Design the gun performance you need on paper, then research those specifications. So figure out what distances you are reasonably going to shoot, figure out which calibers will dispatch the game you are considering, and put together your basic requirements. Then see what's out there that suits your needs.
If I was shooting out to 500 yards and more, like people do on open prairies, that's probably a specialized rifle. It probably has a more powerful scope, and a faster, flatter shooting bullet. My friend shoots a 7mm mag for deer and uses a 4x12 scope. I shoot a slower, less flat 30.06 and have 3x9 scope. There's no reason for me to have a more powerful scope for my bullet performance, but for his bullet performance it's reasonable. That's just an example. You have to decide if you need the high performance of the .22-250 or not.
If you already have a .223 with an appropriate scope for the distances you wish to cover, then maybe spend your money on a re-loader for the .223 and experiment with bullet weights and powder charges making note of the most accurate combinations. (I did that for my Savage 30.06) You may come up with a hand loaded .223 bullet which shoots incredibly accurate. Plenty of people varmint hunt with a scoped .223 out to a few hundred yards.
It's just like motorcycles, you can always spend more money and get greater performance. If money is no object then that specialized gun is just another tool in the tool chest.