Hmmm you want a light weight rifle then go for it
However if you want a light weight then why not go smaller and like the man said 7-08 is good so is the .260 and the .243. All will take Whitetail cleanly with good shot placement
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If you like the longer cartridges then why not the .280 as you say you don't liek the .270. The .280 has a better selection of bullet weights beign a 7mm so ........................
Low recoil ............................ well we are certainly in the .260, 7-08, 257 territory.