In that case, if you intend to shoot past 300 yards or so, a heavier bullet with a higher BC will work in your favor, as long as the rifle has sufficient freebore to accommodate it. I have loaded heavy .224" bullets for F-TR competition rifles for years (i.e. 80.5 to 90 gr). However, those rifles were all chambered with sufficient freebore for the very long bullets, and in F-Class we single-feed rounds, so loading to mag length is not a consideration.
I only recently started loading .224" bullets of lesser weight (77 gr) for a .223 Rem practice rifle that has effectively zero freebore. In the process of doing this, I have pulled a few rounds loaded with 77 gr Sierra Matchkings, just to have them around for chamber/land measurement purposes. I was quite surprised at how deep in the case the 77 SMKs are seated in commercial ammo. The bullet boattail/bearing surface junction is actually seated down around the middle of the shoulder. They really are way down in there. The practice rifle I have with zero freebore shoots the 77 SMKs very well, so obviously having bullets seated that deep is not necessarily a deal-breaker, but will likely complicate the reloading process over time in terms of brass prep, seating depth, and possibly precision. The bullet I have recently been working with is Nosler's new 77 gr RDF bullet. It is a very different animal from the 77 SMK. I primarily wanted to find out whether the manufacturer's extraordinarily high reported BC for this bullet was accurate (it is), but also to work up a load with a bullet shorter than the 80 to 90 gr bullets I ordinarily shoot because of the extremely short freebore of this practice rifle. Initially, the results with the 77 RDF look pretty decent, but I have not finished the load workup yet. In any event, it may be one to add to your list, simply because the BC is so much higher than any other .224" bullets in the 70-77 gr weight class. If the precision I have seen so far holds up, this bullet will represent a real gamer-changer in .224 bullets of this weight class. Nosler also offers a 70 gr RDF bullet with a reported BC that is extraordinarily high. Given my results with the 77 RDF, I have no reason to believe their reported BC for that bullet is over-inflated, either.
The bottom line is that light .224" bullets suffer much more in windy conditions. Yes, you can certainly shoot them out to 500-600 yds, or even farther. However, they don't work anything like as well as the 80-90 gr bullets at those distances when the wind picks up. So my line of thinking for the purpose of target shooting with the .223 Rem has always been to choose the heaviest, highest BC .224" bullet that can be loaded optimally for your rifle (i.e. barrel twist rate and chamber freebore length). Of course, high BC matters little if a particular bullet doesn't group well (i.e. poor precision), so BC alone is not the whole story. Fortunately, you have available to you a very wide selection of .224" bullets in the 69-77 gr range that have proven performance. In your shoes, I'd probably pick one or two, buy a box of each, and then simply test them to see if one looks better than the other. I doubt you'll go wrong choosing any of the suggestions that have been made so far. The good news is that once you've gotten started and worked up a load with one, you can always buy a box of something else down the road and give it a try if you like to tinker with load development and are always on the lookout for something better, as many of us are. Best of luck with it.