You can use just about any die in any press. A die is just a piece of metal that is threaded on the outside and has a specific shape on the inside. They all work pretty much the same.
That being said, there are small differences in design like the small base, full length, and neck only. The BEST resource I have found for understanding the differences is the die manufacturers. I ordered a catalogue from Redding, and there is very good descriptions with cut-away pictures that describe the differences in the dies.
Your press should use the universal thread pitch that most dies have, unlike something like the Dillon Square Deal B that needs specially made dies or the 50 BMG that has it's own dies and press. For .223 rounds that will be used in an AR15 platform, I recommend something that full length sizes. I have used the Dillon .223 dies and the Redding National Match .223 dies. They both work about the same, but the extra support of the case and the micrometer on the seating dies makes the Redding my favorite. (By the way, I got them with a discount, they are pricey).
There is lots of info on neck sizing and small base dies, and all of it tells me that those methods are not appropriate for my reloading on my AR15. I'll let you do the reading to decide that one for yourself.
The other design feature that is important for .223 is the carbide button. It usually rides on the decapping rod. I don't know of any die sets that DON'T use carbide buttons, so you should be ok with any.
You also can mix and match brands, if that is what you want. You can use a RCBS sizing/decapping, Redding Seating, and Lee factory crimp die if you want. The brand isn't as important as the method and care taken to set each stage. Once you get into the details, you may want to look at the Redding S-bushing dies. I have heard great things about them on this site, just haven't needed to try them yet.
Good Luck.