"But which kind of oral appliance works best?"
While there are many differing opinions on this question, there is some interesting research done by Dr Fricton on this subject.
In summary, Dr Fricton and Steve Kraus in his book, Temporomandibular Disorders, agree that-
All oral appliances have the potential to help individuals with TMJ pain.
However, splints only one splint has the greatest potential to help while minimizing the potential for any adverse side effects- as soft stabilization appliances, anterior repositioning appliances, and anterior bite splints have greater potential for adverse events.
The one splint with the best potential to avoid this risk are those that have these guidelines-
1. Full coverage to allow even contact simultaneously during closure.
2. maxillary coverage preferred- (though mandibular coverage may be required)
3. Hard acrylic
4. Thin
5. Anterior portion of the splint provides immediate posterior dislusion in excursive movements
6. Shallow inclines leading into the centric slopes still providing the features stated in #5
7. Avoid aggressive centric relation techniques
8. Appliances should ideally be balanced in more than one head posture (ie neutral sitting up and extension while reclining in dental chair)
In conclusion, any oral appliance can help and has minimal to moderate supporting evidence of reducing TMJ pain. But you may first consider a splint that has these guidelines to minimize the potential of adverse risk factors.