Hi Eric and welcome to the forum.
I had a grandfather who fought in both WWI and WW II and he bought one rifle in his whole life and that was around 1936 and that was a Savage Model 99 in .300 Savage.
Back in the day - he called it his High Power.
It was the finest of 1930's technology and probably has killed Millions of deer between 1920 when it came out and today. MILLIONS
The Savage had a reputation for being a real game getter and would do the job on most big game out to a range of about 300 yards with no problem. Even my dad often said about how my Grandfather - on my mothers side of the family - was the first centerfire rifle - other then his fathers Savage bolt action 30-06 that he had ever shot. Many family members also told me the same thing.
I would compare it to a .308 Winchester because for the most part - they have a lot of similarities. They both used the short action which the 722 Remington was designed for and they both used a 150 gr bullet for deer. My grandfather hunted with Silvertips.
I would make sure that the gun was in good condition, I would take it to a gunsmith and make sure that the trigger was updated because there was a issue with that gun that Remington has a free fix for - which allows the bolt to be opened without taking the safety off. I almost shot the family Blazer one year at camp with my dads 721.
I would check the stock for free float. They have been known to be tight on the forearm end and have been known to move around with changes of humidity and temperature - which is not good for a gun that might have been sighted in when it was 60* and then hunted with when it was 0.
My dad fought that condition with his rifle for many years until a representative from Remington showed him what was wrong and what he needed to do to the stock to remedy the situation.