In my personal opinion the Springfield is the best bolt action military rifle out there.
I have two, a 1903a3 and 1903a4. I like them in un-modified condition. They are accurate.
The CMP has what they call vintage military matches in which they give gold, silver, and bronze metals if you shoot a certain score. The rifles are divided into categories, the M1 Garand, the Springfield, Carbine, and all other Vintage military rifles.
The cut off scores for the metals I mentioned are higher for the Springfield then the others. To make it fair, the Springfield as mention has its own category so the other rifles don't have to compete with it.
They started a vintage sniper match a few years ago covering sniper rifles used before 1955. If you'll check the CMP web site you'll find the scores for the Springfield series sniper rifles (M1903a4 & M1941s) are higher on the average then any other rifle.
The problem with the Springfield is too many of them have been modified or bubba-ed. If I was to find a sporterized or modified Springfield I'd gather the parts and put it back to as original condition as possible.
There are some that say the Enfield's are smoother, maybe, I haven't shot them enough to voice an opinion, The Krag is also an extremely smooth action also. The 'a3s make up for this with better sights.
Don't get me wrong, the Springfield is a smooth fast action, one wouldn't really be at a disadvantage using one in rapid fire.
The Springfield action is one of the most accurate actions out there, not just vintage military actions but even encompassing modern actions.
To point this out, the Army uses the Springfield 'a3 action to make their Mann Devices. These devices were made to test the accuracy of military ammo. They were used to test the '06, 308, 45, and 30 cal carbine ammo.
Waiting to see the pictures of your find. Which by the way is a good buy, You'll find it pretty hard to find a cheaper 'a3 action for $150. A good start to put your rifle back to "as issued" if its been modified.
If you decide to go that route, keep me in mind and I'll help you find parts and with tech. info.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071