If you mean some type of saunctioned short range BR, you would be much better off getting a proper match barrel in an appropriate cartridge. You simply will not be competitive with a factory rifle and recoil will hurt your score even more.
If you want a factory rifle, then I would suggest the 222R, 223, 6PPC as viable choices. Even the 22/250 is not bad IF the chamber/barrel is up to the task. No need to get beat up paper punching.
For LR shooting and a factory rifle, the 223 fast twist, 243, 260, 708 are your best bets. Just look at the many posts on this topic elsewhere.
As to shorter barrels being more accurate? NOPE. The chamber is the most important part of that barrel. If cut poorly, you will have a non shooter no matter how short you make the barrel. Tuning the barrel length happens when you handload so the harmonics of a long barrel are eliminated (at least to the common 26" heavy barrel length).
Now a shorter barrel does have it's attributes but would I cut a factory barrel back to start. NO. I would shoot it first. If it shoots long, it may shoot a bit better short. If a dog long, I would get rid of it and put my money towards a match barrel.
Test the runout of few fired but unsized cases. If over 4thou, bye bye barrel.
So far Savage cuts them straight and throats are nice. Rem has had their problems. SAKO/TIKKA are also consistently good.
Even in a factory class, most short range BR rifles better shoot 1/4MOA or smaller consistently or else you better like the company you are shooting with.
Jerry