Not much information on the 783 HB floating around. But owners of the Savage 12FV (6.5 CM) have consistently reported 1/2 to sub 1/2 MOA straight out of the box, the most accurate I've found.
I'll love to upgrade to a match barrel, but I'll rather dedicate the funds to a decent scope (best I've got now is a $300 Hunting Prostaff Scope) as well as the necessary upgrades to the monkey behind the trigger.
I am a huge fan of Savage as I have said and showed many times. The problem with any factory barrel is the luck of which barrel you end up with. some are not bad, some are not good.
if a shooter picks the best groups and shows the best groups and other assume this is the norm, then the assumption of performance grows.
My experience with many Savage rifles shows the same good and bad I would expect from current manf process. And in every case (except a couple), all of these barrels degraded as they got hot... some hilariously so.
If your shooting needs doesn't require many shots to be fired at a single time, you will be happy with most every brand manf today. But if you want/need to shoot more then 5 rds at a time, you may not be too happy with how the accuracy/precision changes... and that includes the 783 and pretty much every factory rifle.
Choose the factory rifle you like the features and price of... accept it will do what it will do and luck has alot to do with your outcome.
Definitely look at upgrading your optic and other parts that can enhance your shooting experience. Rome wasn't built in a day and what you start with now is just step one on a multi step, multi year process.
Have a goal, budget accordingly, build towards that goal... but most importantly, get out and shoot. The one truism I know is "the more I practise, the more accurate my rifles become"... not sure who coined this but it is very very true.
Jerry