Here are a few recent rifles that I own or have had the pleasure of spending some time with.
Savage - Don't forget they have higher end rifles too, not just the Axis models. Their new 110 Trail Hunter model looks like it may take the lead in the sub $600 range. With that said, I have two Axis heavy barrels, one in 6mm arc and another in .243win. Both will shoot under an inch.
Ruger - Ruger set the bar in "budget rifles" whenever they came out with the American line. Especially with the Predator model. Medium CHF barrels, aluminum bedding block, threaded, etc. I have a Predator 6.5cm that will shoot under and inch all day long. I did put a Timney in it. Now, I have seen some reviews of the new Gen 2's that were kind of concerning. They seem to be more picky about ammo.
Tikka - People fall in love with Tikka's super buttery smooth actions. I have a T3x Lite .223 and it's no exception. It shoots great, however it does tend to be picky about ammo. I will say that the trigger is the best factory trigger I've ever felt. It's right there with my Timney. Down side to Tikka is they seem to be a little behind in the new caliber offerings and threaded barrels.
CZ - Two of my favorite rifles right now are the two CZ Alpha 600s that I have. One in 6.5prc and the other in .308win. Again, a great trigger, CHF medium/heavy barrels, threaded. Probably the least picky of ammo of any rifles that I've ever owned. In terms of quality/accuracy/price, these are probably the best rifles I've ever owned. I only paid $420 a piece whenever CZ was having a $100 rebate.
CVA Scout - I have one in 350 Legend and it has become my go to rifle for deer. Terms of accuracy is simply awesome. It also has a Bergara barrel and a GREAT trigger.
Bergara - They have been making barrels for years. IMO they are the modern day Remington 700 plus some.
Man, the list goes on and on.
I typed all of that, but I am going to say this...
If I were you I would take him to as many gun stores as I could and have him shoulder tons of rifles and see what fits him the best and buy it. It's so hard to get a bad shooting rifle these days, I don't think you could go wrong. Hell, even the new Mossberg Patriots shoot good.
Also.... look up Whoo-Tee-Who on YouTube. He's a great guy that does tons of videos on tons of rifles. Most of his stuff is "budget friendly" stuff, but every now and then he will have a Sako or something like that.
I would also suggest maybe looking at bumping up that 6.5cm to a 6.5prc.