First, I think different posters are talking about different issues/joints. It sounds like OP is talking about the thumb joint by the wrist: the thumb carpometacarpal (CMC) joint. Otherwise known as the thumb basilar joint or trapeziometacarpal joint. That's the most common joint in the hand for painful arthritis. It's caused by repetitive pinching between the thumb and index finger.
That's different than the thumb metacarpophalangral (MP) joint, which is the joint where the thumb joins the hand.
https://arthriticthumb.co/
This is the best splint I have ever had people try for thumb carpometacarpal (CMC) arthritis. It's inexpensive, at about $30. It's fairly unobtrusive, so compliance is good. They're made in Texas. Sizing is measured in inches from the radial styloid to the thumb interphalangeal (IP) joint; almost everyone is a small or extra-small.
But it's made out of leather and textile, so if someone gets their hands wet frequently (i.e. florist) then there's another splint I like, the Push Metagrip.
Push Metagrip Is made out of a plasticky/rubbery material, so it can handle moisture. But it's more expensive at about $80. It's made
by some Dutch company, and then imported by a distributor in NJ. It follows traditional glove sizing (string circumferentially around the metacarpals of rhe four fingers).
Treatment options: behavioral modification (don't pinch as much/hard), oral anti-inflammatories like Ibuprofen/Naprosyn/Relafen/Voltaren/etc, topical anti-inflammatory like Voltaren (diclofenac) gel, thumb CMC splinting, cortisone injection, surgery.
X-rays aren't too important when first dealing with thumb CMC arthritis. You're treating the patient, not the x-rays. It should be fairly obvious to the treating physician what the diagnosis is. But it's worth getting x-rays before going on to surgery, to prevent intra-operative surprises.