Welcome to the hobby.
First of all, follow the advice already given and get at least one, preferably 2 or 3 good reloading manuals.
One thing you don't say is how often and how much you shoot. If you only shoot 100 rounds once a month, it will take quite a while to recoup the expense of a Dillon press with all the accessories. Please don't misunderstand me, I started on a Dillon a little over a year ago and absolutely love it!
I would hold off on a chronograph right now. They are nice, but I would rather see someone spend that money on quality equipment that's more essential.
I do load for my AR-15 and AR-10. Semi-auto rifles take a bit more case preperation than bolt rifles or pistols. For one thing, cases must be full length resized and trimmed every time. Trimming and deburring the cases is the most tedious aspect of reloading for a semi-auto rifle. The only reason that I bring this up at this point is to let you know that you will want a quality trimmer. A hand crank trimmer will take you forever if you have a fair number of cases. An inexpensive option is the Lee setup that has a shell holder that goes into a power drill, and you insert a hand-held trimmer into the case. The Dillon RT1200 power trimmer is VERY nice, but expensive (~ $200 w/die).
One other thing to consider. If you've been shooting Winchester 5.56 ammo or any other "mil-spec" ammo, there's a good chance that your brass has a crimped primer pocket, which means that you'll have to remove the crimp before attempting to prime the case. This can be done witha deburring tool.
All that being said, here's a non-brand specific list of things you'll need.
Press (Dillon 550 will run about $320 new)
shell holder / or caliber conversion kit
caliper that reads to .00x, preferably a metal one, as plastic ones tend to flex a bit.
As far as cost of rounds, here's a very basic rundown.
New .223 = ~$4.50/20 rounds = ~22.5 cents each, or $225.00 per 1000.
Reloading with brass you already have, figuring powder at $20.00 per pound (there are 7000 grains to the pound).
Average for .223 is ~25 grains = ~7 cents of powder, 2 cents per primer, 7 cents per bullet. Now you're looking at ~16 cents per round, or $160.00 per 1000.
These are very rough numbers, but thought I'd give you something to go by.
You might be better off looking at the Dillon AT500 press, which can be upgraded to a 550 later on.
Let us know if you need any other information.
[This message has been edited by Bill in NM (edited March 12, 2000).]