I have owned and handloaded for all three. Still have the .270WSM (Model70) and 6.5x55 (Howa). The other posters are pretty much on the money. If you are shooting deer at reasonable ranges, any of them will work fine. For bigger game, the 270 WSM has a slight edge, but not so much over the standard 270 as to make it more appropriate. (Anything you are comfortable going after with the WSM, could be equally gone after with the standard 270) You could probably go after the same game with the 6.5x55, you probably would be more confident getting 100 yards or so closer.
The 6.5x55 is the most pleasant to shoot, recoil and muzzle blast wise and is notedly lighter recoiling than either of the 270s' (IMO)
But the bottom line is: If you handload, pick any of them. If you don't, find the .270 Win of your dreams and be happy. The standard 270 can also be improved thru carefully tailored loads tuned to the rifle, so it's not like you gave anything up if you later decide to get into handloading. The 270WSM is my favorite medium game cartridge, but I have been handloading for about 30 years. I really like the 6.5x55, but wouldn't buy one unless I handloaded for it.
And as for a previous poster suggesting to stock up when you find reasonably priced ammo for the 270WSM or the 6.5x55, don't hold your breath. I can recall seeing ammo on sale for the .223, .243, .270 Win, 7mm Rem Mag, .30-30, .308 Win, and 30-06. I don't ever recall seeing ammo on sale for the 6.5x55 or the .270WSM. (Other than the online closeout I scored on some 6.5x55 Federal Premium 140 gr Trophy Bonded Bear Claw ammo I got years ago for like $12 a box. Yes I bought the last 5 boxes they had. Still have 4 of them. If I ever go after elk with the 6.5x55, that will be my ammo)
Good luck with your new .270 Win. It is pretty common, but for good reason. Wait until you are handloading before you add your 6.5x55 and .270WSM.
Chuck