Cores: SCH40 and SCH80 PVC will work fine for basic weapons. Sometimes it lasts for years; sometimes it lasts for six months. It all depends on how often you fight and how hard you hit. The trick is that you can't build long weapons with it. For one handed swords, which is all I advocate using it for, you shouldn't cut the core any longer than about 30".
A better alternative would be fiberglass. Solid fiberglass can be bought from electric fence stores, and some farm stores such as Rural King or Farm and Fleet. The most commonly encountered fiberglass rod is 3/8" round. This is okay if you cut the core at no more than 28", but otherwise risks flexing out beyond that. Additionally, because it has such a small surface area you have to be very careful when gluing, as any weaker area is just going to detach.
1/2" round fiberglass is the gold standard for weapons ranging from 26-48". It usually isn't found in most stores, but can be ordered online from stores such as Grainger or Kencove. If you don't have a few people going in on an order, it can be a bit cost prohibitive. However, a single handed weapon built on it will practically never break or flex out.
There are tons more cores and materials, but that's well beyond basic.
Foam: Some types of pool noodle, as mentioned, will work okay for a short while, but they typically don't handle full contact well. Your best bet, if you don't want to spend a lot of money getting started, is to use blue foam. Blue foam refers to
Ozark Trail Blue Camping Pads. You want to make sure you get this smoother looking one, not the bubbled one; two rather different materials. This foam works just fine for pretty much all types of weapons. It requires more padding than more expensive foams, so weapons tend to be a bit heavier or unwieldy when you start making bigger items, but it's economical and definitely has its uses. You can build a basic sword by following the directions found on
http://www.geddon.org, the Belegarth wiki.
Cloth covers: as said, any type will do, really. You can even use some thick pantyhose or dress socks (though they don't look great).
Tape: Duct tape on the handle is fine. Due to the full contact nature of our fighting, duct tape on the blade tends to hit too hard and sting a lot.
Hit Testing: This is really hard to describe online. We test all weapons to ensure that when used in full contact fighting, that they will not cause undue injury or pain. Striking the outside of your calf, strike in a light, medium, hard pattern. At no point should the weapon actually hurt. If you get hit and go "holy **** I never want to be hit with that again," then it isn't safe for full contact. If the impact causes you significant distraction for more than a few seconds (e.g., you're still shaking your head going "oooh, man. Oooh man that sucks), then it's probably too hard.
If you want to build your own gear but don't have access to the materials you want, try ordering the materials from a foam supplier such as Forged Foam, Foametheus, or Warlord Sports. It'll cost more, but you'll get quality materials that you can depend on, and it'll give you an idea of what most weapons in Belegarth look like.
Hope that helps. If you want some videos on some building basics that focus on Belegarth, check out Boffer Basics on
Youtube or
Facebook. I don't have tons of videos up yet, but it can help you get started.