I have loaded the 243 for quite a few years. I found my rifles seemed to like H-380 for things lighter than 80grs, and IMR-4350 for the 100gr loads.
That said, nowadays there are far more choices to be had than there was back in the early 80's when I was really playing around with things. If I were starting now, I would probably look at something like one of the Sta-Ball powders or one of the Hodgdon Extreme line like 4895, 4350, or 4831. I have used them all to build nice shooting loads with 95 and 100gr bullets. The Sta-Ball line I haven't messed with only because I found hat I needed with the H-4350 and also some of the Hybrid-100V, but the latter is specifically loaded in only one of the couple of 243's I have verses the others being used for some load with all of them.
It is a fun round to play with and can be VERY accurate with all of the above mentioned powders. Just go slow and work you way up with all of them. I would also suggest the Accurate or Shooters World 4350's as they are right in the middle of the others and for learning they would make the progress a little more affordable. Once you get a handle on the what's and how's, then start in on the more expensive brands. Also these ARE NOT the same powders so the data cannot be interchanged. Each have their own load data and used within the guidelines will all produce nice loads, start crossing that data however will result in pressures beyond what is recommended. Don't ask me how I know, but it is related to that label which only says 4350, since there are more than one things CAN get get mixed up and it isn't a pleasant experience.
Don't let that persuade you to NOT use any of them or even a couple of them, just keep good notes and denote which is being used. I currently use all but the Shooters World, but my record keeping is MUCH better than it was when I was in my youth.
Bullets - I have a hard time running anything but Hornady, mainly it is a price point. I found they shot well and dropped game well and just stuck with them. There are however plenty of areas going all copper and if I was going to work up a load for hunting only I would probably look into something in the 90-95gr weight of all copper and just be done with it. For standard cup and core bullets though it is hard to beat the Hornady for price and performance.
The biggest hurdle now is finding primers, I see them come and go but the pricing is ridiculous, I might be inclined to find some small primed 308 cases and run with those, just necking them down. At least then you could find primers enough to set up and load for a while. That may not be the ideal thing for a beginner, so if headed that way be sure to consult the powder manufacturer for advice with the powder and bullets your using.
Hope that helps. Be careful and ask plenty of questions.