Ok here is what I have learned going by the rules of youth or reduced loads.
First and foremost the overall best load data can be found over at Hodgdon's site in their Youth Loads using H-4895. Why? Because it allows you to start off with mouse fart loads, and then work all the way up through the powders load range to full power loads using one powder, bullet, and primer combination.
Secondly, IF you have something in like a 6.5, a 7-08 or .308, your going to be better off. Here is why, they can all be had with a ballistic tip type bullet in about the same 100gr weight. Why the BT type bullet, it will open up quicker and more reliably at the lower velocities.
Ok that out of the way. Using the .243 you would be best to go with something like the 95gr weight where you can get one of the plastic tipped versions. As mentioned they will promote expansion at slower speeds. However, you will also want to do some sort of expansion testing as well, just to make sure your on the right track. Another reason is you will be able to get a touch more velocity with a touch less felt recoil.
Did I mention practice....We shot and shot and shot when my oldest grandson started out. I did a LOT of development with my little Ruger Compact in .308. Mainly due to it was already short enough for him to use, and I didn't have a spare stock for any of my .243's, and wasn't going to cut them off just for a couple of seasons of hunting.
He got it in his red knot head at age 3 he wanted to shoot him a hog. Did I mention red head, well yep it is just as hard as it is red. So we started at the bottom of the loads and went from there. Surprisingly using the 125gr BT, I could shoot them into 1/2" groups at 100yds and he after some practice was putting them into around 2" at 50. Two weeks before his 4th birthday he dropped his first in a line of hogs.
Now all that said the first deer he shot with them, simply left never to be seen by us again. We only found a half dozen drops of blood. I know he smacked it good as I was watching it through my field glasses at about 40yds when the hammer fell. I could clearly see the impact right where it should have gone. Throw a hundred yard sprint through river bottom terrain, and and crossing a fence into the mix and she was gone with little trace to follow up on.
Now back to the loads, you can start on the bottom end with the 4895 but I highly suggest working up as much as possible. Even with the ranges your shooting or plan on shooting, the velocity adds energy and expansion. While in most cases with full power loads this isn't as big an issue, it appears to be with the lower powered ones.
If you look through the link below my sig, you can find the grandsons first hog, as well as a buck I shot with an 85gr bonded core in a reduced load in one of the last year or two's hunting pics. He will be a 6 point laying in the back of a Mule 4 wheeler bed. That one almost didn't work out, but luckily it did. It was nothing to do with the bullets not preforming, but everything to do with the tenacity of a mature deer. I really couldn't have asked more from the bullets as they did what they were supposed to do. The buck however was really something.
Hope this helps...