I played with about every bullet you can get for the 243 in handload form, and I use the 95gr Combined Technology BTs for deer, antelope. It's always a bang, flop. I've even used them on coyotes when I ran out of 60gr Sierra HPs, and again a bang flop, with no fur damage as long as you avoid the shoulder blades.

That Weatherby should be a good shootin lil rifle for ya.