I'd suggest .243, regardless of the choices you suggested.
.308, .270 (my preferred hunting calibres) etc will have more recoil than a beginner needs to endure.
The .223, while it has cheap ammo, does not leave much margin for error on deer. It would be fine for goats.
That leaves the .243, which has a great selection of both ammo and rifles. Light recoil so that you will be able to shoot it at the range or bomb up a mob of goats without getting bashed up, enough gun to kill large red stags if you take sensible shots.
Some other calibres have lowish recoil to such as .260 and 25/06 but ammo and rifle selection is small. And ammo probably quite expensive (I reload so not sure on factory ammo prices these days).
Go the .243!
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