It's been a long time since I played without a gameplay mod, but here are my suggestions from what I remember. And let me preface this by saying, there is no wrong way to build your JC Denton. Any build is viable, some will just have more trouble than others.
When you start the game, upgrade Lockpicking, Electronics, and Computers. The first two will get you 25% off a lock or electronic device with a lockpick or multitool respectively, and the latter will allow you to hack computers and security terminals, which basically eliminates the need to find passwords ever. You may want to upgrade Computers to Advanced later in the game, to give you more time to read e-mails, but otherwise that's all you need for those three.
Once you've done that, you MIGHT want to upgrade Pistols to Advanced; the jump in power is very noticeable.
After that, I'd suggest plowing toward Master level in Rifles as soon as you can; once you reach that, the Sniper Rifle has enough power to destroy cameras and turrets, and can also take down MJ12 Commandos (which are big brutes with wrist-mounted cannons and rockets) in one headshot.
From there, it's basically personal preference.
As for augmentations...
Subdermal: Ballistic Protection and Cloak. This gives you the widest range of usefulness; almost all enemies use ballistic weapons, and the majority of enemies you can't sneak around are human.
Cranial: Aggressive Defense System. Explosives are a huge danger to you, and them detonating early is a huge plus. Also, I personally don't like Spy Drone; it drains way too much power for what it does.
Arms: Microfibral Muscle. Being able to lift heavy objects is a lot more useful than doing melee damage, especially with the awesome melee weapon you'll get as part of the storyline.
Legs: Speed Enhancement.. Run Silent just doesn't do that much, and you can crouch with Speed Enhancement on to move quickly and silently.
Eyes: Vision Enhancement. This is personal preference. I'll admit it's really cool to see detailed information on enemies, but I prefer being able to see through walls (at Tech 3 and 4.)
Torso: Aqualung, Regeneration, Power Recirculator. Aqualung is more useful than Environmental Resistance because there's a LOT more situations where you can swim and there's no rebreather than there are situations where you need to cross an environmental hazard and there's no HazMat suit.
Regeneration is mostly personal preference to me, and the alternative aug in that cannister (Energy Shield) is good too, but I'd rather be able to heal than take less damage from energy. Aggressive Defense System can detonate explosives and (I think) plasma bolts, and enemies with flamethrowers are very uncommon.
Power Recirculator is again personal preference; I'd rather save my biocells. The alternative, Synthetic Heart, burns 100 energy per minute (which is a full charge) in exchange for boosting the performance of your other augs (but not beyond their max level) which in my mind is not worth it.
Weapons: I always take one heavy weapon, usually the GEP Gun, for dealing with enemy mechs.
Two pistol-grip weapons are a good idea; I would suggest the Stealth Pistol and the Mini-Crossbow. The Stealth Pistol is silent, although it requires a double-tap to the head to down most enemies, and one tranquilizer dart will eventually down any human enemy, no matter where you hit them.
I also take a Sniper Rifle, the melee weapon you get as part of the story, an Assault Rifle, and either an Assault Shotgun or a Sawed-off Shotgun. As I mentioned, the Sniper Rifle can destroy cameras and turrets (and some doors) at Master Rifles. That melee weapon is extremely powerful, to the point that you can destroy bots with it if you're patient. The Assault Rifle is a good mid-range weapon and has an underhand grenade launcher, and the Assault Shotgun is excellent at close range. The Sawed-off Shotgun actually does more damage per shot, but has a much slower rate of fire. Both are capable of taking down bots with 12-Gauge Sabot rounds.
Whatever you've got left over in your inventory is personal preference. Grenades, miscellaneous items, and so on.