A Winchester is a great choice. To be honest you have your caliber bases covered. But all of your rifles are relatively heavy hunting or varmit guns. A FW is not especially light by modern standards, but would make a better rifle to carry around for general hunting than any of the others you already have.
A 243 is an option, but it is so close in between the 25-06 and 22-250 that I wouldn't go that way. I view the FW as the perfect big game hunting rifle for the guy who actually gets out and climbs up and down mountains for big game. Not too heavy to carry, not too light to shoot well.
I know you already have a 308 stealth rifle, but a FW in 308 would be a completely different rifle that could share ammo. One in 30-06 with good handloads will all but equal your 300 H&H in performance, but be in a much lighter, more compact package. I'd go with one of those 2 with what you already own. If you just want to branch out and have different calibers I'd look at 7-08 or 270.
A 243 is a darn good deer round, but for general hunting where larger game may be encountered you can do better. It is also a good varmit round, but you already own better varmit rifles.