" It will be a lower end rifle like a remington 700 "
The Remington 700 can compete with any firearm on the market, but to answer your question.
Check all functions for loose bolt,loose safety, loose clip , metal firmly attached to stock etc.
Open action or remove bolt and look down barrel in bright light. Bore must be clean and you should see grooves.
For a scope mounted rifle, I always take a Bore Sighter with me. With a bore sighter you can instantly check to see if the scope adjustments are working.
All scopes"look the Same". Some are junk and others are very high quality
The scope mounts should not show signs like being modified,shimmed,screws forced or broken etc.
Having a friend along that knows rifles and possibly owns a bore sighter if rifled scoped, would be a great asset.
My son has a Remington 700 BDL in 30.06 and it is extremely accurate, right out of the box.
Check the bore and the area in front of the chamber. Look for signifigant errosion. Inspect the locking lugs on the bolt, the should have even wear on both lugs, if not then bad accuracy could result. Bring along a headspace checker and see if you could close the bolt with it installed, if so the headspace is excessive.
My apologies for calling the 700 a bottom of the line. Let me reword that to say more what I was thinking. I'm looking for a simple rifle not looking for fancy engraving or a really nice stock, something that will shoot reliably and most importantly is an affordable price. I was also looking at at remington 710, but new.
Thanks for the advice, now if I could ask the same question but about shotguns, also advice about choke selection for duck and some upland game.
My choice is the Rem. 870 Express 3" magnum. I don't think you will want to use the same choke for duck and upland birds though. I'd get the Mod., Imp., and Full chokes so you can vary depending on what you want to hunt, but I'm no expert that's for sure. So I may learn something from this post also
Shotgun choke tube selection can depend on a few things like game, weather, distances, shot type, caliber, etc. but if you want the multi-purpose tube I'd have to go with the modified. It is the jack of all trades for tubes and works well with the steel shots used in waterfowl today. If you are turkey hunting you will want full choke and cylinder choke for doves.
What do you do with those empty nylon feed bags or dog & cat food bags? Can you say recycle? I use them for target practice for the youngsters. Take your empty shopping bags, stuff them into an empty nylon feed bag. You can also use old clothing or rags, (but put them in the bottom so it doesnt get top heavy). When your bag is full, fold the top over, punch some holes into the top and zip tie the top shut. Paint, draw, paste, or have the kids decorate their new target. Set it out 10 or 20...