How to decide on what priors distributions to use for parameters?

Bad Initial Energy usually denotes a problem with the model, not the sampler. NUTS is robust and state-of-the-art, and a good thing is that it spits out warnings when something’s wrong. Switching to an older algorithm, like Metropolis, when you don’t have to doesn’t necessarily mean the problem is gone – it’s just that the sampler doesn’t warn you about it.
So my advice would be to figure out why your model spits out a Bad Initial Energy – you’ll get a better model in the end. Here, your model uses very well-known and continuous distributions; this is NUTS kingdom :crown:

I’m not sure I understand the question: both Metropolis and NUTS are MCMC algorithms.

There are very good resources to introduce you to the Bayesian workflow and methods. I listed some of them here.

Hope this helps :vulcan_salute: