If you plan on mostly deer hunting with the gun and an occasional coyote, I'd recommend the 25-06. If you plan to do more coyote shooting and an occasional deer here and there, I'd recommend the .243. In any case, either is capable of doing the job. The .243 will give less recoil and is a LITTLE more pleasant to shoot, IMO....

These are all good for both- .243,257 Roberts,25-06,257 Weatherby.Not a dog in the lot but the .243 leans a shade more towards the varmint side IMO than the others.The Weby is the fastest/flatest shooting of the bunch.The Roberts is a great old cartridge but not many makers offer that chambering these days.Really cant go wrong with any of these.Some mentioned the .270.While it will certainly get the job done it's really a bit overkill on varmints.

.243 Win., .25-06 Rem., .270 Win.

I agree with driftrider in recommeding the 25-06. IMO the 25-06 is abetter deer round and a muchmore versatile cartridge overall.

Any of the 6mm's with the 243 being my first choice.

There is a lot of .243 lovers and all the power to you, it is indeed a great cartridge and I will not debate otherwise.
As far as the varmint side of calibers the .243 is one of the best choices when you are considering jumping up, to use it for Deer, and probably the minimum IMO.
I chose the .270 for the simple reason of misplaced shots on deer. The .270 will allow for some "Murphy's Law" that happens while hunting.

As an "example" of my claim... While hunting in TX back in 2007, a gentleman gut shot a deer with a .243. Now I'm not claiming that it would have died quicker with a .270, as mentioned it was a bad shot, so let's get that straight. However, after recouping the deer the following day, some 500 yards away, the guided said... In his 28 years of guiding, "the heavy majority of the deer that are wounded are from people that come to camp with a .243". He has always recommended @ least a .270 for this reason, but doesn't enforce it. As he too says "a well placed high percentage shot from a .243 will down a deer just fine".

So there you have it, my opinion why!

If your are a marksman that has never compromised a high percentage shot.
OR
If your deer has never moved / twitched while squeezing the trigger, then a .243 is your poison, a little extra can never hurt though???

.243 or 6.5mmSwede

6.5X55 Swedish fantastic groups and long range when fired from a Husqvarna M96. I also own Ruger, Savage, Remington and Browning rifles and the Husky is the most accurate.

well i think if your deer are not to big all you need is a 22-250 i have been killing deer yotes and everything texas has to offer and no problems and you can reach out there and touch them with a 55-60gr bullet

I have a .300 WSM for the big stuff and a .243 for deer and smaller.

I used to shoot a .22-250 as my small caliber, but it was too light for deer. .243 is the best of both worlds