What he said. ^

Another vote for the 243Wssm.

The 25-06 is a perfect choice.

.25-'06!!

243,25-06,257 roberts,260 rem

.22's aren't a legal caliber for goats here in Wyo. Considering flat shooting, ample knockdown, ease on the shoulder, ammo availability,
etc . . . The 25-06 and nothing else! Make sure and get a good scope to at least 12 power!

Another vote fr the 25-06 for what you want. There are other rounds that are good but IMHO the 25-06 is the best choice when taking into account availibility and performance out to 300 yards. Wally World to you're local shop odds are they'll have it in stock whick can't always be said about some rounds mentioned here and gets the nod over the 243 at longer ranges.

I'm curious... Are speedgoats harder, about the same, or easier to killthan a whitetail? If it's about the same, and you assume a minimum of 1000 ft lbs needed for a humane kill, the .243 is a 300 yard rifle and the .25-06 is a 400 yard rifle. For yotes, you probably need less, so both will likely suffice out to 500 yards. The trajectories for a 100 gr. .243 and a 120 gr. .25-06 are remarkably similar. Not more than about a 1 inch difference over 500 yards.

you answered your own question ipsc. The 25-06 gives a bit better performance with a heavier bullet. I never said that the 243 is a bad choice it's just the 25-06 is a bit better and that's why IMHO it gets the nod over the 243.
Personally for varmits and yotes my choice is a 22-250 and a 7mag or a .30 round for everything else with the exception of the great bears and Africa where my 375 H & H would be the gun of choice for me.

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I'm curious... Are speedgoats harder, about the same, or easier to killthan a whitetail?
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Antelope are easier to kill than whitetails.