I decided to get an old 6.5x55 rifle to play with, an old sporter where it wouldn't matter if I got a little bubba on it.
The gun is probably older than all of us and all the numbers match, out of the box I started with about 8" groups. With a few different loads that went to 5".
Knowing this was way out of touch I turned my attension to the rifle, well the crown was shot and the stock needed bedding.
I tried recrowning the barrel myself, popped on a synthetic stock and bedded it myself plus added a Bold trigger for kicks. The money I spent working on it was less than the ammo I expended out of it.
I must admit I also started reloading for it at that time and now have two loads that group under an inch at 100yds with hunting bullets.
I also found with reloading that starting at the minimum suggested load and working up is a great idea, in my experiences the heavier loads are not the most accurate.
Do note I would never consider myself a precision shooter, others here are.
Good luck