I've played through New Vegas many different times with many different types of characters, but I never really invested in trying my skill in hardcoe Mode extensively. I am interested because it provides something different to do and it does seem more realistic. I know I will need to pay attention to my hydration, stimpacks healing over time, ammunition having weight, companions dying permanently, limb healing and balancing out my rad a bit better, but are there any tips, or other things I should know about?

Not really. hardcoe mode in New Vegas isn't really all that Hard. It's not going to affect your game too much, and it's not going to be that difficult providing for your basic needs. The one thing you might have to watch out for is your ammo. It will now have weight so you'll need to be a bit more discriminating about what you lug around.

Boost your survival skill and check the recipes available at the campfire. There are some important ones - Cactus Water, Snakebite Tourniquets, Gecko Steaks that are easy to learn and extremely useful for healing as well as reducing starvation/ dehydration. You may want to get your Medicine skill up to 40 to make doctor's bags, and better healing items will be useful so replacing stimpaks with super stimpaks may be a smart move.

You'll get the hang of it.

Pretty much what david said, though I will add that you can make healing pultices with Honest Hearts that do the same thing as doctor's bag and healing powders combined. and there is also Fiery Purgative with Lonesome Road that heals radiation, and cures poison too.

I suggest looking into the DLC if you do not have them. Overall, boost survival and play a bit smarter in combat when it comes to hardcoe mode, maybe even leaving companions behind when going to dangerous areas.

I only play hard core these days (and for quite some time). It generally isn't all that difficult, except when you really need to heal up and can't find a bed forcing you to rely on stimpacs, water, or food for healing. Which of course almost always has a cost in rads...

Helpful items include the Vault 13 canteen (which really won't keep up with your demand in many instances) and some sort of bedroll. I usually take the "skilled" trait, which helps get survival up to that critical 25 so you can cook gecko steak, at least. A decent Medical or science skill also helps, so you can fix the "Fiery Purgative", "Healing Poultice" and the "Snakebite Tourniquet" as previously mentioned.

Some mods are also very helpful, like the "Bottle that Water" mod or the "Realistic Portable Tent" mod.

Good luck, eh?

I already have adopted more of a "sneak snipe" kind of combat style, which I imagine could lessen my damage taken in some encounters depending on the enemy. I have never really delved too far into the survival skills before, but I understand how much they will probably help in this mode so I will try it. The tagged skills I chose are Guns, Medicine, and Barter or Speech I think. Should I replace one of these with Survival? I know it won't matter much once I start putting in skill points, but still. Oh and gecko steaks sound good right now!

Having survival tagged saves a lot of the headache of putting points into it, as it starts at around thirty that way. Food/survival items also stack, so they become more valuable than stimpacks.