RSA is often the algorithm of choice, as it is now rather old and survived going through a lot of scrutiny. You can't go wrong chosing it. The 256 variant is good enough IMO as SHA256 is nowhere near being broken.
If you care about the size of the message, which you likely do in JWT, you may want to use ECC. It allows for significantly shorter signatures while being as secure as RSA in theory. In practice, the problem is in implementation. There have been spiked curves in the past and a lot of problems with implementation such as off-curve attacks. It is more likely for ECC to have mistakes in implementation IMO.
The PS algorithms are based on RSA but apparently are modified to have a reduction proof. I would not give too much stock in the proof and as it is relatively new and more complicated, implementations may have problems. I would not choose these.
So in the end, I would chooose one of these two depending on what level of security you need. ES256 is probably the beter choice for most webapps.
PS: Either way, you should obviously make sure your jwt library is being updated in a timely manner in case there are security related bugfixes.