I believe you mean the 257 Roberts???
It's a great cartridge, providing you get one with a 1-10 minimum twist rate.
If you get one of the rifles with a 1-12 or 1-14 twist rate, you will likely have to be happy with bullets of 100 grain maximum
Many of the earlier rifles have 1-14 twist rates. Same goes for the 250 Savage, which can be loaded to very similar velocities, with just about any given bullet weight.
In modern rifles, such as Winchester M70, Remington 700 and even the Savage 99 or custom 98 Mauser actions. Both cartridges can be loaded very close to the factory specs of the 25-06 in any available bullet weight.
I sold the Remingto Mod 700 Classic I had in 250 Savage a couple of years ago. But I did retain the Remington 700 in 257 Roberts.
The ease of converting 7x57 cases, if needed, is just a great option as it works for the 6mm Remington as well.
That was off topic.
OP, cheap is in the eye of the beholder.
Wanting to shoot ''cheap'' at this point in time?????? You're a bit late to the show. Maybe two years late.
One cartridge that will do everything you list, is the 7.62x39.
There are all sorts of options for different rifles that the round is chambered in and depending on your budget, which from the gist of your post is limited, quality can be mediocre to high end.
Howa, Zastava and Ruger, to name a few make very decent bolt action rifles, chambered for the cartridge. All are strong and the cartridges can be loaded much hotter than book specs, without issues.
The 7.62x39 will duplicate 30-30 specs, even with 150 grain bullets.
I fnally settled on the Howa 1500 mini action, after trying the Ruger and Zastava, which I found both to be very rough with poor triggers. Bit more expensive but well worth it as it shoots all bullet weights from 100 grain .308 diameter to 150 grain of the same diameter
The bore is .309 and it handles bullets of .312 diameter, up to 150 grains without issues and shoots all of them acceptably for hunting Deer out to 250 yards.
