27 x 1 1/4" were the most common size, back when 27" wheels were a standard in the US. There were narrower 27" tires (27 x 1 1/8" and 27 x 1"), but they were much less common. So almost any frame that was made for 27" wheels tires has frame clearance for 27 x 1 1/4" tires. As for suggestions, most of the 27" tires discussed in this thread are 27 x 1 1/4.

If you want wider tires. check the clearance between the chain stays before you buy the tires. It might not accommodate wider than 27 x 1 3/8". 27 x 1 3/8" tires existed, and many frames that were made for 27" wheels were made to accommodate 27 x 1 3/8 tires. But since 27" tires wider than 1 3/8" were almost nonexistent, there was little reason to built a frame with space for wider 27" tires.

I have a Maruishi TA18 that was sold with 27" tires. It's a touring bike, which one might expect to be made to accommodate wide tires. But it was designed for 27 x 1/4" tires, because that's what existed, and it won't fit tires any wider than 1 3/8" nominal width, and those only barely (depending on the model and the actual width). With 700C wheels, I have more choices of tires, but the limit is still the chainstay spacing. I can fit some 700C x 38mm tires, but only barely, with no more than 2 mm chainstay clearance on each side of the tire, and a chain tug to hold the axle perfectly aligned.