$350.00 max, 300 yard max shot. I'm thinking Leupold Vx-3i, 3.5-10 x 40mm. Seeing this for about $320.00. Will be putting this on a .308, likely a Tikka Lite.

Hard to beat Leupold for a classic hunting scope.

Works for me.

Burris Fullfield II

I think there are a bunch in that price range that are excellent scopes. I think most are going to hold zero fine. I would look through several an see which had the best clarity and the longest and most forgiving eye relief. Also look for the reticle you like best. I also think if you just go get a VX3 that would be fine too

The Burris FF comes in at half of your budget and stands alone at that price range. If you’re spending the budget get the VX-3

Burris FF is a nice scope. Bought one for my brother a couple of years ago. If you can wait Midway has Vortex Viper 6.5-20x50 on sale for around $350 occasionally.

I feel like a pure hunting scope within that range, I'd make clearest glass and large objective lens the two highest criteria over things like zoom or reticle (which are two features that can get expensive fast).

I was in the search for something similar with a bit more targeting shooting features for my 6.5 grendel. For myself, I narrowed it down to:
hoping to save enough money for https://www.opticsplanet.com/trijicon-accupower-2-5-10x56-30mm-riflescope.html (and if the fantasy football gods are with me maybe I still will. I love trijicon glass and 56mm sounds awesome for low light)
there was something called a bushnell trophy legend 2.5-15x50 i thought a year or so ago.
this seems like an awesome hunting scope https://www.opticsplanet.com/nikon-prostaff-7-2-5-10x50-quick-focus-riflescope.html <- edit: just saw howl's post. I think his are better suggestions

Ultimate I went with a 4.5-14x44 primary arms arc-2 moa becasue it was a store front blem I haggled them down to a good price in person. I won't reveal the number but way too good to pay up even thought it wasnt't exactly what I wanted.

Two good ones, I hunt some place where shots may be 50 yards max and others where shots can be a bit longer, out to 300 or so. Love having the extra field of view 2 or 2.5 X on the low end for the extra field of view on a whitetail or hog hunting scope. For just making the shot I do nto feel under scoped with the 2X7 scopes that reside on some of my favorite rifles

Probably one of the SWFA

There are lots of truly great scoped out there now, but I just cant get enough of Nikon's these days. The eye relief is second to none, and the glass is exceptional for the money