The main thing is knowing your trajectory and the distance to the target. (As usual.
A .243 is plenty big enough. Good shot placement with an '06 won't hurt any meat.
I fell into a deal on a ranch just north of Marfa, Texas, getting a nearly-free hunt. We found a nice, cooperative patient buck of some 15", so I busted him. Took the shoulder-mount part over to the taxidermist at El Paso. Eventually Mr. UPS arrived with the mount. I'm still chuckling about how the "stretch job" makes him look much larger than life. Heck, I've seen 150-pound mule deer that weren't that broad across the shoulders!
Not bad for a critter that dressed out at maybe 90 pounds...