I've built two #1 Rugers in 505 Gibbs and the advice provided thus far should be strongly heeded. As Raff noted, the front hanger on the #1 limits the barrel diameter. You need barrel weight to balance any recoil reducers in the stock. The best way to achieve this in a .577, since the hole is so big, is to use a long barrel. I'd be looking for a 28" finished length and the largest diameter that will clear the hanger, with minimum to no taper to the muzzle. Because of the short action length, overall length with a 28" barrel will not be ungainly. My weight goal for a 577 would be 13 pounds. Don't forget to modify the butt stock to take the recoil. All the nice radii on the rear of both tangs must be relieved and, on my jobs, I relieve and use steel bed to reinforce the flat recoil surfaces at the front of the stock. A muzzle brake is a personal choice, but I put them on the 505s. The muzzle brake can be machined to act as a recoil stop for a banded front sight, which works to perfection. Good luck.
Otto