I reload 5.56 as part of my business:
I'll give you some pointers:
The best press for reloading 5.56 is the Dillon XL650 with their powered trimmer.
Outside of that I would recommend the Redding Big Boss as it's a great press for a really decent price.
The Redding Competition series dies are great and I use them for all of my reloading needs. You'll need a crimp die as well.
The best hand load for the 5.56 cartridge is the MK262 Mod 1. This is what I recreate when I reload 5.56. The key is to use the Sierra 77 grain bullet with cannelure. You can use numerous powders that respond well in the 5.56 cartridge (AR Comp, etc.) but, the MK262 Mod 1 has muzzle velocities ranging form 2,700 and 2,750 fps.
At that velocity you need to make sure your cartridges are in great shape and that they are necked to the same dimension every time. In addition, you need to use a high quality primer; I use the military CCI #41 primers.
You have to remember that the 5.56 cartridge is a high pressure cartridge, so don't use it in a .223 chambered rifle and don't load a 5.56 load in .223 brass just to be safe.
Work your loads up using a chronograph (I recommend the Magnetospeed V2) until you hit your target velocity...while checking your cartridges and primers for deformation.
Most once-shot military brass (you can determine if it is once-shot if the primer pocket is still crimped) will work well...that's what I use and sell. Lake City and Federal are my personal favorites.
The MK262 Mod 1 is a great cartridge out to 700 meters and through a 1/7 or 1/8 twist barrel on a MK12 SPR it is flat out deadly with an experienced trigger puller.
As far as prepping your cartridges, follow these steps: (1) de-prime, (2) clean with stainless steel media in a wet tumbler, (3) dry and de-crimp, (4) full length body size, (5) neck size, (6) measure, (7) trim cartridge length to 1.750, (8) de-burr case neck, (9) prime, (10) load powder, (11) load bullet to cannelure line, (12) crimp, (13) cartridge gauge check / chamber check, (14) magazine check, (15) fire and chrono.
Let me stress again, reloading is inherently dangerous...load slowly and work your way to your target velocity and also check group size. You may find a good load for you rifle that is below your initial target velocity.
Hope that helps.