How fun for you to have to choose a new caliber and cartridge!! I was in your shoes a few years ago. At that time, I owned a 30-06 (my first big game cartridge) and then I got a 300 WSM when I moved to Colorado. Once I put a brake on the 300 WSM, it became a joy to shoot. It's my dedicated elk rifle. Then I got the reloading bug, and started spending a bunch of time on this website doing research. The 7 STW forum caught my interest, and I bought one. It's become one of my absolute favorites. So much so, that I burned the barrel out of it because I shot it so much. The modern day equivalent cartridge is the 28 Nosler. I have a brake on my STW and it's less recoil than my .243. It's a frickin' tack driver, too. So, look for a lightly used STW on this site or buy a 28 Nosler.
If you want a 6.5, decide how much horsepower you want first. I bought a 6.5-284 Norma (from Smokepoles). It's probably one of the best 6.5mm cartridges since it is very efficient, extremely accurate, low recoil and get's the most out of the 6.5 round without being overbore. If you want a flamethrower, look at the 26 Nosler or the 6.5-300 Weatherby. The 6.5 Creemoor is probably the cheapest to shoot, has plenty of factory ammo options, low recoil, great accuracy and will handle most the game you want to hunt to a max of 5-600 yards.
Hell, a 30-06 can do everything you want. Load it up or down in bullet weight. It's extremely versatile and easy to load for. I've kinda rediscovered my 30-06 lately and love that caliber once again