So I looked up my serial number on the Ruger website and found out that it was made in 1978. Then I looked around and found out that I might have a Wilson barrel. So I wondering if it is a good barrel of if its one of Rugers crap barrels?

Shoot it and find out. Can.t say if its crap or not. I seen them shoot great and I seen them shoot not so great.

How does it shoot

Crap is as crap does.

As p dog says, shooting it will tell the tale. Just be sure to give it a fair chance by trying a few different types of ammunition/loads and assure that the bore is clean, actions screws appropriately tight, and scope good. I've seen a number of rifles assigned to the scrap heap because of "bad" barrels which had some other easily solved problem.

If it's a Wilson bbl. it's one of the better ones put on Rugers in the late 70's. Wilson makes very good barrels. They are not hand-lapped match grade barrels but they are well made and they normally shoot real good. I have one on a re-barreled Model 70 that shoots very well. It's a 243 and shoots loads that it likes down around 1/2 moa.

What caliber?

While some folks have had problem guns of that era, it has not been my experience. I've had a thing for the tang safety guns and have had something more than 30. I think I have six right now. They've all been decent or better shooters. Give it a try with a number of different brands and bullets. Please keep us posted on your results. They are my favorite rifle.
Good Luck
Bfly

The older Rugers can to challenging. For example, I had 2 tang safety 77 RSIs in 243 that were 6 serial numbers apart, 78-447x2 and 78-447x8, that were as different accuracy wise as night and day. -x2 would shoot good groups, but -x8 wouldn't group at all, even when I installed the barreled action in a 77 RL stock. After being rebored from .243" to .264" and rechambered to 260, it has been a much more accurate rifle.

The best advice has been given:"Go out and shoot it"

And so was the advice about finding any sources of inaccuracy, such as bedding, barrel touching something in the stock, bad scope, etc, is good.

But, the Wilson barrels of that period were not the match quality Wilson barrels of today. Ruger wanted cheap barrels and they got cheap barrels from their vendors. Some are very good, some are not so good. You have to shoot it to find out, but don't start out with the idea that you have a "bad barrel" because it will become a self filling prophecy.

The 2000's Ruger M77 Tactical I have has one of Ruger's hammer forged barrel and it is an excellent barrel.