The first thing you need to buy is a current handloading manual or three. There are lots of bullets and powders available now that weren't around 35 years ago. Speer, Hornaday, Sierra and many other component makers have published loading data books. The possible combinations of powder, bullet and primer in .223 Remington / 5.56 x 45 are nearly endless.
Dies for your press are a matter of personal choice. Most of my die sets are RCBS but I have some Hornadays, too, and Lee will fit in the same presses, all using the standard 7/8-14 size threads. Your press also likely uses standard shell holders. I would recommend that whichever brand of dies you buy, get a shell holder from the same maker.
A good handload for the .223 I like for most plinking uses a 55 grain FMJ-BT bullet, 26.2 grains of Winchester 748 powder and either CCI, Federal or Winchester small rifle primers. This data is published by Winchester Olin and they say it duplicates their factory 55 grain FMJ load in pressures and velocity. 748 is a ball powder and meters accurately in a powder measure. I like Winchester, Hornaday and Privi Partizan 55 grain FMJ bullets, and have shot a lot of others (Speer, Sierra, Nosler) with excellent results as well. Honestly, I don't shoot well enough with my Colt AR-15 Sporter, my Remington Model 7 bolt action or my employers Colt M-16-A2 to determine if one of these good bullets is actually better than the others.