Personally, I identify the chambering, barrel and bolt that I want first, as these are the most important, the next on my list of importance is trigger, gas block and recoil spring/buffer. The rest are mostly just personal fit/visual/comfort.
Chambering: .22lr, 9mm, 223/5.56, 7.62x39, 300 BO, 6.5 Grendel, 6.8 SPC II, .458 Socom, .450 Bushmaster. These cover a good cross section of what the AR15 can do. There are a lot more other chamberings out there, but these have shown themselves to be mainstays in the market in their value and performance relative to what their use will be.
22lr.: plinking, small game, training children
9mm: plinking, training, self defense, suppressed, training children
.223/5.56: plinking, training, self defense, hunting
7.62x39: plinking, training, self defense, hunting, suppressed
300 BO: suppressed, self defense, hunting
6.5 Grendel: distance, hunting
6.8 SPC II: self defense, hunting
.458 Socom: suppressed, hunting
.450 bushmaster: suppressed, hunting
These are generalities, but that is how I lump them. My preferences are bolded above, haven't decided between .458 and .450. The .450 has started to win out in my book simply because there are some bolt actions being chambered in it currently.
Barrel
What type of shooting are you going to be doing? Bench, stalk hunting, stand hunting, 3 Gun, Self-defense, Ammo Burner
Pistol, Carbine or Rifle determines barrel length.
This will dictate length, profile, material and gas port location.
Gas port locations Pistol = ~4"; Carbine = 7.5"; Mid-Length = 9.5", Rifle = 12.5"
Bolt
The next most important item that has varied degrees of quality
Steel Type: 8620 (most are through hardened), Carpenter 158 (surface hardened), 9310 (need to get the heat treat right, but is stronger than C158), Aremet 100 (premium and the price tells one so)
Finishes: phosphate, nickel boron, chrome, nitride, etc.
Inspection: Magnetic Particle Inspected (MPI), High Pressure Tested (HPT), Shot Peened (more of a process of releaving stress than an inspection)
Features: Extractors should be of quality parts, this is a more frequent failure prone part on an AR15, one can upgrade extractor parts for >$10 and it's worth one's while.
I would never consider a 8620 as it is through hardened so it won't absorb the shock of the impulse leading to cracks, Carpenter 158 is a great duty level of performance as it is surface hardened which leaves the underlying metal malleable to absorb shock impulses.
Carrier
Type: Semi-Auto; Full-auto, lightweight, adjustable gas
Steel Type: Typically 8620 or Carpenter 158, some 9310
Finishes: phosphate, nickel boron, chrome, nitride, etc.
Features: Grade 8 fasteners, staked or non-staked gas keys
Here there are options on carrier type have a lot to do with weight. The full-auto carrier is just that, it would be sufficient to operate in a full auto M16/m4 it has extra weight in the tail as well as fully shrouded firing pin (right BCG in picture below) the left two BCG's are variations on semi-auto carriers. A lot of the choice here would be predicated on what type of carbine/rifle you wish to build/buy. For a bench gun, huting gun, a lighter weight semi-auto carrier would be nice for lowering the weight of reciprocating mass. If it's to be a self-defense, or ammo burner, a heavier weight carrier would be preferable. I personally, don't like the
unshrouded firing pin versions, but that's more personal preference.
Adjustable carriers, there are two companies that I know of that have adjustable carriers, Gemtech and Primary Weapons. They have an adjustable port typically just below the staked portion of the gas key on the ejection port side of the carrier. I don't have any personal knowledge of their utility.
Trigger
I'm sure you know what a good trigger feels like as you don't know much about AR15 but I'm assuming you know plenty about other rifles/triggers.
Combat trigger, single stage, two-stage, adjustable, binary, drop in.
Value triggers: LaRue MBT (my favorite), ALG
Premium triggers: Geissele, Timney, ELF, Hiperfire
Specialty triggers: Fostech, Franklin Armory (both are binary triggers) I don't have any experience with these as they don't trip my trigger)
Gas Block
A key design of a quality barrel is a correctly drilled/sized gas port, this is where differences can be seen in budget barrels versus quality barrels.
Type: Low Profile, A2 gas block, adjustable
Low Profile is for gas blocks that reside under free floating rails, these are either clamp style or set-screw into a dimple on barrel. I prefer to have an alignment dimple that the set screw sets into.
A2 Gas block is a great option for a rough use carbine, it's dependable and very strong, and provides a front sight. Downsides are it pigeon holes you into certain hand guard types that are most typically non-free float, you can get a set screw type A2 gas block and utilize a free float but that seems dumb to me, its a compromise on the A2's ruggedness.
Adjustable gas blocks are great for those who want to tune a bench rest rifle, hunting, suppressed, etc. There are varied types of adjustable gas blocks, some just restrict flow, and some will bleed off extra gas at the block itself.
Recoil Spring/Buffer
Recoil Spring: Standard coil, flatwire, silent capture springs
Buffer Weight: H (4oz), H2 (4.5oz), H3 (5.5oz), H4 Tungsten (6.5oz)
The standard coil while it does what it supposed to, there are better options. Flatwire or silent capture springs are a great way to get added performance and comfort. The first time one shoots an AR15 chances are they will notice the SPROING noise right at their ear. Most do not notice it as they get familiar with the AR15, however there are options on fixing/mitigating that noise while adding some performance/handling benefits. Greasing a spring will help dampen the noise as well and is a low cost option to get some benefit.
Handguard
Type: Free-float, non-free float
Features: Pictinney, M-Lok, Keymod
Materials: Aluminum, carbon fiber, polymer
The biggest performance difference here would be free-float versus non-free float. Free floating hand guards minimize contact with the barrel which will improve accuracy. Downside to this would be not as robust as an A2 sight setup and a non free floating hand guard. Pictinney, M-Lok and Keymod are personal preference, they all have great 3rd party support, pick one and go with it. I prefer M-Lok as I don't like the look of Keymod, and like I MagPul.
For lightweight hunting rifles the carbon fiber hand guards are a great option to lose weight out front.
All the other stuff is gravy on the meat and potatoes.