In my honest opinion all hunting rifles are "hunting" accurate, meaning they can easily kill a deer sized animal out to 200 yards.
The .243 and .25-06 are great choices for varmints/deer. I will not suggest any others... The .243 has a more mild recoil ant the .25-06 probably offers a little more range.
You should know that the "cheap" lines of Weatherby's are actually not Weatherby's, they are Howas, nothing necessarily wrong with that, but they are a less expensive gun, so you really aren't getting a Weatherby.
If you have the resources I would heavily suggest the Sako 75 hunter. You will not be disappointed. All those other guns are fine, but the Sako is in another league and not really comparable. You will get a silky smooth action, a beatiful piece of wood, and amazing accuracy, and decent trigger right out of the box.
The rugers, remingtons, winchesters, etc. are all great guns, if you want to save a few bucks and get one you probably will be happy, but feel out all of them first and then compare it to a Sako 75 hunter or a Weatherby Mark V (two great guns).
The 25.06 fits your bill perfectly. More range than the .243 for both varmits and deer. Yes a little more recoil but worth it. Bull barrels are good for multiple shots at varmits like praire dogs. They heat up less quickly so the point of impact doesn't change as fast. For deer the heavey barrels are less important and I would only consider them if I was hunting from one location with longer shots and not walking around. The 25.06 is avalible from most makers.
botha 243 and 25 06 will do the job, there is little ballistic differenece between the two. as for rifle Ive been partial to browning, the are of excelent quailty. if you go browning or whinchester have a look at the new 25wssm or a 243 wssm. they offer higher speed so flatter tragectory. barrels well bull barrels are heavy so not very good to be packing around all day, but do offer more shots before your barrel starts to really heat up. these are big game cartidges so they will heat up your barrel either way, just leave your bolt open and the barrel will cool faster.
The 243 is a varmit rifle that can be used for deer. The 25-06 is a deer rifle that can be used for varmits. If you will use it most for deer, go with the 25-06. No contest really.
Personally, I'd recommend the new .25WSSM. It has .25-06 ballistics with the advantage of being able to have a smaller rifle if you wish and an extremely short, fast action. The WSSMs are proving to be extremely accurate as well. The only downside I could see to it would be the availability of factory ammunition, but since you plan on reloading, that shouldn't be a problem anyway.
I'm going to buy a rifle that I will be used for everything from woodchucks to whitetail. I would like to buy a good one. Probably a .243 or 25-06, but I'm open to suggestions.
JamesB summed it up pretty good; "The 243 is a varmit rifle that can be used for deer. The 25-06 is a deer rifle that can be used for varmits. If you will use it most for deer, go with the 25-06. No contest really."
I'd go with the 25-06, and have to agree, hard to beat the Sako 75 Hunter for quality.
For less $$$, I guess I'd go with a Ruger MkII. However, you will most likely need to have the trigger adjusted on the Ruger, or replace it with a Timney.
ok, my varmint deer rifle is an Olympic Arms PCR-8 mag AR-15 chambered in 25 WSSM
with Olympic's excellant SUM (stainless ultra match) barrel, it'll give 90% of the turnbolt varminters a run for they're money in the accuracy dept. Pricey but its awesome
RR
James B put it pretty well. if you handload consider the 6mm Rem, same bullet as the 243 but a little more zing. the 25-06 will be hard to beat for a varmit/deer rifle. If you want a quality rifle consider buying a used rifle in good shape , then use the extra money putting a custom barrel and trigger on it. maybe a nice stock too.