Number of iterations

If your Markov chain behaves well enough then effective sample size controls the error of your MCMC estimators, such as the mean (see for more details). So you want to generate enough effective sample to be sufficient for your application. In general there is no unique answer.

For example, if I all I want to do is crudely locate the mean within the marginal posterior distribution then error[f] ~ sqrt{ Var[f] } / 3 should be sufficient and that implies

\sqrt{ Var[f] / ESS[f] } = error[f] ~ sqrt{ Var[f] } / 3
3 ~ sqrt{ ESS[f] }
10 ~ ESS[f]

Typically 100 effective samples allows for a more precise evaluation of the posterior properties.

Just keep in mind that all of this holds only if you have a central limit theorem, which means also checking for divergences, Rhats, and the like.