On paper the 270 kicks a bit less than a 30-06. My shoulder can't tell the difference. The 270 was made by necking a 30-06 case down to 0.277 inches. It holds the same amount of powder. Bullet weights are typically lighter than typical 30-06 weights, but they do overlap and even so are close enough to ignore from a recoil perspective.
The 308 is a short action round designed to approximate the 30-06 performance and with 150 gr bullets it does. The 06 has better performance with heavier bullets due to its larger case capacity. The 308's recoil is not bad, but different than an 06, as it typically is loaded with a different burning rate of powder. Best I can describe it is that to me the recoil feels somewhat sharper than an 06.
The stock design of the rifle will have more of a noticable effect on recoil to you than which of those 3 calibers you pick. If possible, try to shoot a variety of different rifles to see which ones you like best, regardless of caliber. Look for a stock with a straight comb and little drop, meaning the stock comes straight back from the grip without dropping down very much. This lets the rifle recoil straight back, rather than pivoting up and smacking you in the cheek.