I have 223, 204, 22-250 and 220 swift. For varmints out to 400 yds if you are limited to one, 223 or 204 w 40 grain will do best in the wind. 223 will be ok. Lightest recoil will be 204.
IMO the best and most cost effective will be a 223, there is available off the shelf ammunition from inexpensive plinker rounds to match grade rounds. Also there is a much greater range of factory loaded bullet weights for the 223, I have seen factory loaded ammo from 35 gr to 90 gr, although for PD shooting the 40 gr has no peers IMO. Check the price of factory loaded 204 ammo versus factory loaded 223 ammo and you will see that the 223 ammo has much more availability and is less expensive, since you do not reload that should be a prime consideration.
If you should decide to start reloading at a later date you will find easy and more inexpensive components for the 223, whereas components can be a bit harder to find and often more expensive for the 204. 204 brass availabity in particular can be spotty and expensive sometimes.
Lightest recoil with the 204 - NO. If you check the loading manuals and look at the amount of powder being burned in the 204 and 223 in most cases the powder amount is so close that it is not even an issue. The only way to get less recoil in the 204 is to shoot the 32 gr bullets and even then it is only about a half ft-lb less recoil.
204 - Using the Hodgdon on-line reloading data for the 204 with 32 gr bullets the average powder charge is around 29 grs ballistics recoil calculator the recol energy is 2.5 ft-lbs.
Using the JBM using the 204 data for the 40 gr bullet the average powder charge is around 28 grs. Using the JBM ballistics recoil calculator with a 9 lb rifle recoil energy is 2.8 ft-lbs
223 - Using the Hodgdon on-line reloading data for the 223 with the 40 gr bullets with an average powdr charge the recoil energy is 2.8 ft-lbs, the same identical ft-lbs of recoil as the 204.
The less recoil for the 204 was pushed by the manufacturers and gun writers when the 204 first came on the scene but facts are that it is impossible to change physics - if you are shooting the same weight bullet and using the same powder charge the recoil will be the same. I am not just using the calculators to prove a point - I had Tikka T-3 sporters in 204 and 223 the rifles were virtually identical. I also had Cooper Varminters in 204 and 223 they too were virtually identical with weights being to within an ounce of each other. I let other people shoot them without telling them which caliber they shooting and no one has ever been able to tell a difference in recoil. Only one could tell the difference between the 204 with 32 gr bullets and the 204 with 40 gr bullets, there is a difference but it is so minor as to be a non-issue.
As far as barrel life the 204 will be a bit shorter because you are burning the same amount of powder through a smaller diameter hole. Also the 204 is operating at around 55,000 psi - the 223 around 48500 psi, the higher pressure of the 204 will shorten barrel life in comparison to the lower pressure 223.
Out of my 223's I expect around 5000 rounds of 1/2" or less groups before I start seeing uncalled flyers, the 204's gave me around 4000 rounds of sub-1/2" or less groups before I started seeing uncalled flyers. For a lot of shooters this is not relevant because they will neve shoot 4000 rounds in their life but for me it is a real consideration because I generally shoot 3500 - 4000 rounds per year.
I am sure that there will be those who disagree and that is ok, but just remember - the laws of physics cannot be repealed or suspended.
drover