The 243 will have zero issue making it to a mile!!!!!!!
The 6BR/wildcats is about 3/5 the case capacity and is doing very well in the 1000yd BR game. The 105/107/115gr bullets are the best but not necessary.
The twist in a factory 700 barrel will not work well with these bullets but there are many other choices. Top of my list would be the 87gr Vmax and 95gr SST.
If the rifle/barrel/load is well assembled, you will have no issue going as far as you have scope adjustment for. These bullets have quite high BC so you will need way LESS adjustment then the typical 308.
I had no problem hammering clays at 750yds using the itty bitty 6BR and 87gr Vmax. The 243 will launch these 200 to 300fps FASTER. So you will very similar ballistics to a 105/107gr bullet going much slower - will fly flatter but drift about the same.
The big reason you don't see more 243's in competition is throat wear. When you are shooting a few thousand rds a season, barrels wear out too fast. That is why the trend towards the 6BR and modified 22/250 cases. Less powder burnt at much higher pressures to get the same muzzle velocity with reduced throat wear.
If a 308 can be used to 1000yds very effectively, the 6, 6.5 and 7mm are much better.
Bed the action properly, get rid of that barrel hump in the stock (no rubbing on the barrel), lighten the trigger as low as you can tolerate, good optics, good rests, good dies and loads/bullets, have a lot of fun plinking at whatever distance you care to go.
Save your money for barrels and bullets cause LR shooting is way too addictive.
Jerry