Yep, got one that started out looking just like that! My first rifle, in fact, when I was 14. Dad bought it off the widow next door for $20 (seriously!).
He then sanded down the stock, taking the sharp edges off the those forearm inlets, put ebony caps up front and on the grip, and a recoil pad.
Can they shoot? Oh, yeah!
About 25 years ago a friend talked me into going to a turkey shoot in Lloydminster. He loaded up a couple boxes of ammo for me ahead of time, and the day before I went out and zeroed it 100 yds. Had a Bushnell Sportchief 3x9 on it at the time.
Entered a 100 yd, 3 shot competition along with 9 others, many of them packing some very serious looking shooters. All done, three of us scored 30...but I had the tightest group, and took home the bird.
Then I entered a 200 yd shoot, 3 rounds. Crosswind was horrible. Two guys using 22.250s didn't even hit the paper, that's how bad it was! I scored a 27 out of 30, and won again!
By then the guys with the fancy Sakos, Weatherbys, and the like seemed to be a tad somewhat curious about my old BSA Enfield! Naturally, I then put my two turkeys from my two events into the pickup and rode off into the sunset. Heh! Does it get any better than that!!!
Anyway, a couple things about 'em...
You may find that it doesn't feed reliably, as the bolt may slide by the next round without picking it up. I was told by one smith that this is because the magazine is designed for .303 Brits, which are a rimmed case, and therefore require a wider box. Consequently the 30.06 rounds stagger a tad bit too much, and don't always slide up enough for the bolt to catch the rim. To my knowledge there's no fix for this. If you cycle the bolt with some "authority", the cartridges always will snap up into place. But working the bolt quietly and softly, maybe not.
However, I came up with an idea of my own. I took a bleach jug, carved up a shim from it, and mated it to one of the inner walls of the magazine with a bit of glue, shiny and slippery side out. This did seem to help. I think doing both sides would have helped even more.
That's FWIW.
The other thing to watch for: Yours is drilled for scope mounts, too. That same Scopechief of mine turned out to have a problem. Point of impact shifted about 5" between 3x and 9x...??? Sent the scope to Bushnell, who called to tell me the tube was bent for some reason, check the drillings/bases on my rifle. (They repaired it no charge anyway!)
Yep, the rear of the action had been poorly machined by BSA, I assume to get rid of the military style rear sight set up, and was causing misalignment and torquing the scope.
The solution to prevent this problem even possibly happening (on any rifle, for that matter) is to use Burris Signature rings. Their unique design automatically compensates for alignment, and thus protects the scope. No lapping required. Or re-machining of the mounting surfaces.
Lastly, there are aftermarket triggers available for these, notably Dayton Traister for one. Eliminates the terrible two stage pull. Be sure to mention that yours is a BSA sporterized 30.06.
These are very good rifles, with lots of potential. IMHO, they're definitely keepers!
Mine, after full custom job by Wilcox Gun in Lumby, BC...