You don't indicate which state you intend to hunt. Check your state laws. There may be restrictions on the case, caliber, and power level.
If you are in IL then neither the .243 or .25-06 are legal for deer because the rd has to be at least .30 cal and a bottleneck case cannot exceed 1.4" in length.
Good point.
In Iowa the regulation is as follows:
Handguns: Center-fire handguns .357 caliber
or larger, shooting straight wall ammunition with
an expanding-type bullet. Minimum barrel length
for all handguns is 4 inches. No shoulder stock or
long barrel modifications are allowed.
Only the following center-fire cartridges may
be used: .357 Magnum, .357 Maximum, .375
Winchester, .38 Super, .40 S&W, .401 Powermag,
10 mm Auto, .41 Remington Magnum, .41 Action
Express, .44 S&W Special, .44 Remington Magnum,
.44 Automag, .444 Marlin, .445 Super Mag,
.45 ACP, .45 Colt, .45 Super Mag, .45 Winchester
Magnum, .45 Silhouette, .451 Detonics, .454
Casull, .45-70 Govt., .460 Rowland, .460 S&W
Mag, .475 Widley Magnum, .475 Linebaugh, .480
Ruger, .50 Action Express, .50 Linebaugh, .50
Beowulf and .500 S&W Mag.