Dead Space

If you are on PC, disable vertical sync! It cuts the frame rate and causes noticeable input lag.
Consider playing on Hard. Once you beat the game you unlock Impossible difficulty and you can create a save for a New Game Plus, but you can't change the difficulty (and New Game Plus on Easy or Medium is boring as hell). Even if you don't care about playing the game a second time, Hard is a suitable difficulty for more experienced gamers.
The difficulty curve of the game doesn't take huge leaps. Don't stockpile heaps of med-kits and ammo for a rainy day, sell things off and spend those credits.
If you're running out of ammo too quickly, try carrying fewer guns. The game drops ammo based on the guns in your inventory, so two guns = twice as much usable ammo as four guns. Find your favorites and stick with them.
Upgrade/power node advice: upgrade one weapon first, then the health on your rig and a second weapon, then everything else you'd like.
Upgrading air, stasis, and kinesis is a waste until you have nothing else left to upgrade. All of the vacuum sections can be beaten without air upgrades and air canisters (the asteroid section in chapter 4 is tricky but it gives you a timely air canister). You shouldn't need more than 60 seconds to beat any of these areas, and in the few cases where you do, there are oxygen rechargers all over the place. Any time you need stasis to pass an area there will be a stasis recharger nearby. Kinesis range is only convenient in a few spots and should be the very last thing you upgrade.
In most of the chapters you'll find a door that can only be opened by using an upgrade node. Nine times out of ten the goodies behind one of those doors are at least worth the price of the node, plus whatever schematics are in there. You'll at least break even, so go for it.
Make slow, careful progress through the levels. If you rush in blindly, you will die a LOT. There is no real time limit to any part of the game.
If you run away from Necromorphs or their path to you is blocked, they will find a way into the room you're hiding in. They don't need to use doors.
Do NOT use your melee attack unless absolutely necessary. It should be a last resort only.
Save frequently and in different slots. The game uses checkpoints so deaths are never all that punishing, but it's possible to get yourself into an impossible situation and it's a good idea to have an earlier save to revert to.

General weapon advice

Everyone has their personal preferences when it comes to weapon choice, but most agree: the Plasma Cutter is great, the Flamethrower is terrible.
Give every weapon a try. Just save before buying a new weapon, test it out for a bit and simply reload the save if you don't like it (or just sell it off and get some credits back).
Every gun seems to starts out feeling underpowered, but becomes a ruthless death machine when fully upgraded.

Weapon Details

Plasma Cutter: You can literally use this starting weapon for the entire game. It's the most versatile weapon in the game. Be sure to hit the Secondary Fire button to change its firing pattern from vertical to horizontal, it's usually more efficient.
Line Gun: The king of turning enemies in a heap of limbs. A great panic weapon, it decimates at close range and the line will pass through enemies. Not very good at long range or at dealing with enemies that jump around. The mines dropped by Secondary Fire are very powerful, it just takes some timing/time (use it on Necromorphs that are attached to the wall for example).
Ripper: The buzzsaw is a fun one-on-one weapon and also cleans up swarms of little critters nicely. Downsides are that it requires you to get very close to an enemy and it's easy to get ambushed when you're sawing something. Very ammo sufficient and excess ammo can be sold for a decent price.
Pulse Rifle: This assault rifle chews through ammo, but when you upgrade its damage it will become a reliable medium/long range weapon. It is a less exciting alternative to the Plasma Cutter. Much like with the Line Gun, the alternate fire is great to blow up those Necromorphs attached to walls.
Flamethrower: Seems cool but it does not do the damage nor have the stopping power required of a close range weapon.
Force Gun: The shotgun of the game. You have to be at a certain range for it to be effective. Too far away and it does nothing, but if you're too close it loses some punch too. Once you develop a feel for the range and where you have to aim on the enemy's body, you can kill most enemies in 1 or 2 hits. The best part is that it pushes enemies away from you and knocks them on their ass.
Contact Beam: A laser that fires charged shots. The ammo is expensive and it requires a steady aim, but it delivers in terms of damage. A great weapon against tougher creatures, tentacles and bosses. The alternate fire is a panic button to allows you to clear your immediate area.