What's the best treatment for arthritis of the joint at the base of the thumb?

Short Popp ensplint. Antiinflatory medication such as Aleve (naproxen) or Ibuprofen will help along with a splint or brace. Look for a "cool comfort neoprene support". Cortisone injection can help a bad flare but does not influence the long term outcome.
Several. Treatment for this type of arthritis, carpometacarpal arthritis, can include wearing a splint, taking anti-inflammatory medications (such as Ibuprofen or naproxen), or a steroid injection.
Arthritis. The best treatment is what is right for you! Rest, antiinflammatories, injection of corticsteroid, splinting, activyt modifiaction or surgey, its depends a lot upon who you are, what you do, how you tolerate pain. Arthritic treatment is treating the symptoms and can't be the same for everyone.