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I agree completely with Skiprr on good rings and mounts. I'll confess I'm not as fastidious, though. I've never lapped rings, for instance. I did procure a foot-long piece of 1-inch diameter stainless steel, though, and I go through the steps of getting my rings aligned using that instead of the scope. Scope doesn't go into the rings until alignment is as perfect as I can get it (sans lapping). And a reticle alignment tool is definitely a must.

You said this is for a deer rifle. What range and terrain do you expect to hunt? My go-to deer rifle for the past 20 years wears a 2-7X, which is perfect for hunting the woods of PA and NY, and it's quite capable out to 300 yards on deer-sized game. Even for a beanfield rifle, I'd probably opt for a 3.5-10X40. I've bought a couple of used Leupold Vari-X III 3.5-10X40s in the low $300s. I'd rather an excellent used Leupold than most of the others out there. But that's just me.