In my experience the 257is a wonderful cartridge. Mine is an AI,but that's a minor preference.For most purposes,its unnecessary.
What you are somewhat up against,it is a "square peg" cartridge in a time of "round hole" rifles.
In the days of the 257,the receivers of choice were milsurp bolt actions,or the Winchester/Remington equivalent.The magazines,rails,etc were set up for the Mauser cartridge case derived rounds or 30-06 derived rounds.
As the 257 is a necked down 7x57,it fed and functioned fine.The Mauser length box gives plenty of room to long seat bullets.
If you find any bolt receiver ideal for these cartridges,you can easily build a very nice hunting rifle.
You are free to have your preferences,but the 257 works via precise shot placement.In that way,a bolt offers plenty of follow up.Generally,you will have a lighter,more accurate,and more dependable hunting rifle with a bolt gun.
Most (not all) 6mm Rem rifles would work well to convert.Some 6mm Rem rifles were built on true short actions,like the Rem 600. You CAN do that.But if you do,you will be deep seating lighter bullets to a short cartridge length. That decision by Rem may have contributed to the success of the 243.
Rem twisted the 6mm barrels for light,short varmint weight bullets,and stuck the 257 with anemic 117 gr round nose (shorter) bullets.
You might have to build it,as the 257 lacked the sales volume to sustain factory chambering. I'd avoid the 257's built on 308 length actions myself.You don't have mag length for long seated 115 and 120 gr bullets.
If you choose a 308 length action,bolt,pump.or semi,we are back to the square peg and round hole.While I am a .257 fan,I also know the 243,260 Rem,7-08,and 308 are also fine cartridges.
Any of them will serve as well as a .257 . Its easy to have those in a short action repeater.
A 260 Rem and a .257 R just are not that different. Seven thousandths of an inch!! Velocities are equivalent. More bullet types are available for the 260.
My point,with the available choices,and not creating unnecessary trouble for yourself,Think about that square peg/round hole thing ,get her done,and go shoot!