1. The pulse gun is your best friend. Great for robots, roboscorpions, turrets, etc.
2. The advanced LAER with mods is a great general purpose weapon.
3. Anything can kill the lobotomites, I used That Gun a lot for this or the LAER. At long range, the Gauss rifle works well or Christine's sniper rifle
4. The undead harnesses are tougher, but the LAER or any high damage weapon seems to work for them
5. The Nightstalkers were really hard for me. I tried all kinds of thing before finally adopting That Gun with AP ammo (or Christine's rifle at long range)
6. Lots of weapon repair kit fixings around the place, I collected them and had more than I could ever use by the time I was done.
7. Find all the chips for the sink. Not only will all the extra gear (MF and Energy cells) from breaking down appliances and pencils and clipboards help you but it will make a better base later for general wasteland exploration
8. I brought a variety of weapons with me, keeping the weight down to a reasonable level so I could switch off between weapons so I wouldn't run out of ammo in any one weapon. I shot more with weapons I could easily repair.
9. I took the jury rig perk and took the Vault 34 security armor. Very good armor, and you can repair them with jury rig with any of the lobotomite clothing so I was always in good repair. The little blue halos (can't remember the name) were also repairable with any kind of eyeglasses or goggles.
10. Stealth is not strictly necessary but is useful to limit combats and when you get to the stealth suit quest, being able to sneak well is really useful.
11. Explore the Think Tank area. Lots to loot there and they don't seem to mind.
12. Get the force field mod for the sound emitter early so you can disable force fields when you're exploring generally.
Like I said, I'm not a great player but that's the advice I'd give. Having found bomb collars in the internment camp, I REALLY wish (having failed to get through Dead Money) that finding them and examining them could give you a way to disable the collars. That would actually have been pretty cool.