The .303 British in a SMLE is definitely NOT a "mistake" in a fun to shoot rifle and caliber! It served the British Empire as the standard battle rifle for more than 70 years and continues to serve sport/meat hunters by the tens of thousands. In Canada, for example, sporterized SMLE rifles continue to bring home more venison, moose, elk, bear, and reindeer than all other rifle calibers combined! Power wise, it is in the .308 Winchester class. The cartridge may be 120 years old, but it's game performance is as good as it ever was.
It is easy to make accurate jacketed and cast bullet reloads. Case life can be short, but there are various "tricks" to getting the most out of the .303 SMLE. Neck sizing only, factory duplication loads only, and "clocking" (indexing the case for every shot) will extend case life.
The .243 Winchester in a Savage 99 is a fine rifle. A real advantage of that caliber is lighter recoil and faster follow-up shots if needed. Reloading presents no special problems. If high velocity is your goal, the .243 Win is a champ, and will double for deer sized game as well as varmints.
The choice is certainly yours to make: a battle-proved rifle and caliber or an equally game-field proven rifle and caliber that is more modern.
HTH
John