Foreword:
This guide is going to go through the steps on how to build a good character, and have many modular cookiecutter builds as examples, but the idea is more to show how to build a good character build, than to list viable builds.

A Word to the newbies
You're probably wondering what order to raise stuff, so I'll add my bit on that too here: Max out your attack skill first, then the attributes for it, then INT+PER if you're going crafter, then endurance, then armor use, then coordination, then other skills. You'll get more and more AP freed up as you get to higher levels to flesh out your build with. Work on your dodge before going to S2, and I suggest doing so no sooner than level 18 and preferably waiting until 20+. Dodge can however wait until you're at least level 13 or so.

Step 1:Combat or crafter?
Simple step: if you go crafter, you max out INT and PER, otherwise you ignore INT and only max PER if you go ranged.

Cost for crafter: 280 AP

Sidenote: a main mutation build may only wish to take an attack skill to 120 or so, more on that under mutation builds in the advanced builds section.

Step 2: Pick a weapon choice.
In most cases this means melee, pistol or rifle, though you may pick more than one, as a hybrid build, in general you pick one, and at most raise melee as a backup to one of the ranged choices(particularly rifles).

For ranged you'll want max dex and per, for melee max str and coo.
This means a total cost of 363 AP(2x140+83)

Step 3: Defense
Next step, how much defense do you intend to get, generally it is a good idea to max them out, but for some builds a lesser amount of defense is acceptable, to fit all you need/want into them(especially for crafter builds).

Max defense: Max coordination, endurance, dodge, armor use; caveat: you only need 164 armor use, so it will cost two less than a normal maxed skill, total here is 444/437 AP (2x140+83/76+81)(second number after dash is max dodge for melee build with no PER)
Good defense: Here, the sweet spot for having a little less defense, but still quite high, is to reduce your max-level coordination and endurance by 8, leaving you with a max dodge of 154 and armor use of 150, I recommend this for ranged crafter builds. Total cost of 352 AP.
Decent defense, poor health: Max coordination, normally maxed perception from a previous choice, gives 166 dodge, 135 armor use, poor hp, and costs a total of 290 AP. Suggested as a decent choice if you are maxing cha/social, and pick up telepathy to match that(has maxhealth buff).
Good health, shoddy defense: Max endurance, armor use to 135, dodge to 110 or 124 depending on PER. Total cost of 272/279 AP(depending on PER).
Minimal: No points in defensive stats, max dodge(124, with max PER, since this is NOT recommended for melee), armor use to at least 90, but will probably want to keep it maxed until end levels to wear better armor sooner. Total 107 to 127 AP.

Step 4: Support skills and Mutations
This is where it gets a bit tricky, and even more modular.

Charisma builds
These are only really suggested if you want to have max social, perhaps to be your clan's shopping guy for expensive and rare mats.
Typically you'll have CHA+PER maxed, and 1-3 of the following skills, in rough order of importance:
Social - 83 AP to max, buy stuff cheaper, minor buff/debuff abilities.
Telepathy - 76 AP to max with no willpower spending, healing skill with maxhealth buff and a 10m range damage+stun attack.
Group Tactics: minor buffing/debuffing and minor healing

Mutation builds
These builds have maxed WIL, and will want to max PER, INT and possibly END, as you might imagine, they get very AP heavy and thus tend to pick one of the cheaper defense choices.
You'll want at minimum: Max telekinesis, max thermal, max sonic, and either max nano-manipulation or empathic(or telepathy, if you also max CHA).
Patho-manipulation is also quite nice for it, after that it gets a bit blurry.

Medic builds
Buffer subclass: Maxed first aid, usually combined with crafter since first aid is primarily INT.
Combat medic subclass: Maxed empathic and Telepathy, of course any old class can have these, but probably not as dedicated as having both.

Just your average mutant:
Brief listing of what the mutations do, and their primary stat(all have willpower as secondary), shamelessly stolen from darksilver:
Nano(INT): self-heal; hp/sta/gamma regen; targetable gamma->hp transfer; rez; self DoT remover; hp/sta->gamma siphon
Thermal(PER): DoT; DD+DoT; melee dmg shield; fire resist debuff;snare+coo. debuff; self DoT remover+heal
Enhancement(INT): armor buff; team armor buff; elemental buff; hp&sta regen; bod&ref.&min saves buff
Suppression(PER): gamma siphon; attr. debuff; stamina siphon;DoT remover; AoE dmg; self convert gamma into hp&sta
Sonic(PER): DoT; AoE dmg+stun; snare+coo&per debuff; DD; AoE armor debuff, armor buff
Telepathy(CHA): targetable HoT; group HoT aura; targetable maxhp buff; team AoE DoT remover; rez; DD+stun
Patho-Transmission(END): sta drain+end debuff; AoE DoT; DoT; snare+dex&coo debuff; str+end debuff; disease+radiation+chemical+poison resist buff
Primal(STR): coo&per buff; run speed buff; str&end buff; dex&per buff; str+coo buff; self sta regen
Empathic(END): rez; targetable DoT remover; dmg shield; self heal; targetable heal; team hp&sta heal
Telekinesis(INT): armor buff; AoE knockdown+DD; run speed buff; team armor buff; self gamma regen; root+dex debuff

Step 5: Final check
This step is basically figuring out if you can afford what you're planning. What the AP costs will be. It is technically possible to get over 1100AP without doing AP runs around the faction wheel or repeating missions btw, but it'll take quite a while to do them all anyway. I'm guessing the grand-total AP available is somewhere around 1150-1180AP, but to squeeze out those last few AP will take you months extra, so for the purpose of this guide, I'm going to count 1100 AP as more or less the max, but don't despair if your build goes slightly over. Base AP without missions is 880 AP.

Costs
Attributes cost 140 AP to max.
Skills with both attributes maxed costs 83 AP to max.
Skills with primary attribute maxed costs 76 AP to max and takes it to 152.
Skills with secondary attribute maxed costs 62 AP to max and takes it to 124.
Skills with both attributes at minimum cost 55 AP to max and takes it to 110.
Skills with attributes left at 75(8 under max) take 75 to max, taking them to 150.
Skills with primary taken to 75 and secondary maxed costs 77 to max and takes them to 154.
Armor use, with either attribute maxed and the other at minimum takes 67 AP to take to 135(no reason to pay 68 to max it).

Sample build, my current pistol combat build(which I've taken to 45) has currently:
Max DEX, PER, COO, END = 560 AP
Max Pistol, dodge = 166 AP
Armor use 164: 81 AP
Empathic, Sonic, Thermal taken to their no-WIL maxes of 152: 228 AP
Telepathy taken from 55 to 70: 15 AP
Telekinesis taken from 55 to 88: 33 AP
Total: 1083 AP

I have 1088 AP, with 5 unused, I'm not done with all AP missions yet, and haven't even started doing the archive missions for the three sectors(24 AP there alone).