Elected - you have the problem of two chambers claiming legitimacy and potential deadlock, and also the problem of potentially having the same short term view as the other elected chamber.
Appointed - who gets to appoint, on what criteria, who are they beholden to ( ideally unsackable once appointed - I want them to feel free to say what they really think ).
Inherited - Very unlikely to represent the population. No quality filter. Potentially a culture of service built up - and free to say what they think.
Random. - More likely to represent the population. No quality filter.
You can obviously have a mix of all or any of the above.
In my view, the ideal second chamber would be full of people of experience, who are beholden to nobody (unsackable), that represented a broad range of views, with a culture of service.
I'm against a fully elected second house - as that's not really adding anything different to the first house. Appointed has worked quite well in the past, but it has become more and more abused recently as the elected politicians have two much control.
It's tricky - perhaps some sort of mix.