^ Bingo. Read, read, read. As far as AR reloading, Natchez has an RCBS AR reloading kit that has dies for all the major AR calibers (5.56/.223, 300 BLK, 7.62x39, and maybe one more...) that'd be a good, ready-made setup.
Dillon is great, but getting parts can be tricky, especially now while things are still not yet cooled down in the ammunition/arms world.
I'm a big fan of Lee- I've had my Lee turret press for years and thousands of rounds. It's far from the fastest, but it's compact, inexpensive, and I can switch dies and calibers quickly and easily. Plus, parts are almost always available, and dies from other companies will fit it (I have a smattering of Hornady, RCBS, Lyman, etc. in the mix, and everything fits).
As far as what all you'll need:
Dies (5.56/.223, and any other caliber you want to reload)
Shell holder for your calibers
Priming tool with shell holder for your calibers
Powder funnel (not REQUIRED, but very damn helpful!)
Press of some sort (from the Lee Hand Press at $25-30 all the way up!)
Case trimmer (5.56/.223 almost always seems to need trimming, especially mil-spec cases)
Micrometer (digital, for case length prep)
Scale (again, not REQUIRED if you do volumetric loading [Lee has powder dippers- I use these for plinking rounds- competition rounds I use the scale, plus I run a check-up on the powder dippers on the first round of every volumetric batch], but recommended)
Case cleaner (also not required, but 5.56/.223 tends to be fairly dirty, and I like NOT putting old carbon, dirt, etc. back into my guns!) and media
Boxes for ammo (you can re-use your commercial boxes, or use specific reloading boxes. I'm a huge fan of MTM- cheap and easy!)
Bullet puller (also not required, but you WILL screw up, and it's nice not to have to summarily throw out components!)
Primer pocket swager (most mil-spec 5.56 cases will require the primer pocket to be swaged prior to reloading)
(more than one. I use Lee and Hornady primarily, but the others are good, too. There's an AR-specific reloading manual I have that I got on Amazon that's been pretty darn good, too)
Load stickers and a marker (to help you organize your rounds, and remember what you put together)
Powder trickler (not required, but helpful. Spend more here for one that has good reviews, and doesn't leak like a sieve during changes/dumping! Ask me about that one...
Primers (some say AR-specific rounds MUST run military-type primers, some disagree. I've run non-military-type primers with no issues, but that does NOT mean that's the best idea)
Powder (buy AFTER you read through your manuals and find some good combinations- start with ONE pound until you find what you like best, THEN buy in bulk when you find out what works- not the other way around!)
Cases (either once-fired [check with local ranges- many will either sell you bulk, once-fired brass, or let you clean up] or fresh. DO NOT NECK SIZE ONCE-FIRED BRASS FROM OTHER RIFLES! Only your own
Bullets (.224 diameter for 5.56/.223. Make sure they're not for other .22 caliber rounds- .22 Hornet, .22-250, etc. as the length may cause issues)
Bullet lube (used if you don't run the cases through a carbide/titanium die)
There's probably something I'm forgetting. The basic rule of reloading is read, read read. Plan on screwing up. Take your time, and measure twice (or more) before you test-fire. I never recommend a progressive press to a newbie (or re-starter- no offense!), as the temptation to burn through rounds as quickly as possible makes the chances of issues (double-charge, deep-set bullet, inverted primer, etc.) more likely, and reduces the chances of noticing that mistake as well versus a single-stage or turret press. As I mentioned, I am a big fan of my old Lee turret press- slow, reliable, and easy.
The last thing I'll say is get carbide dies where able- they'll save you $$ in the long run in terms of bullet lube, case wear & tear, and the inserts supposedly last longer than plain steel (haven't reloaded THAT many cases in any caliber that I've had issues yet!).
If you have any questions, I'm far from an expert, but it sounds like we have some other experienced folks here, and we're all willing to help! Cheers- Mark W.