You might want to take a look at the password generators in existing password manager tools, such as LastPass. As @RonBowes says, there is no one-size-fits-all policy, and the sad fact is that many sites have policies that mean you can't use a very strong password (Until a few years ago, Wells Fargo bank only permitted 6-8 case-insensitive alphanumeric characters for its online banking, to give the most egregious example off the top of my head) so you can't even just flip between a couple of highly-secure policies such as "very long but only alphanumeric" vs. "relatively short but selected from all typeable characters".
Generally speaking, longer passwords are safer, mostly regardless of the character sets used. For example, randomly selected case-insensitive alphanumerics are still more than 5 bits of entropy per character; a 20-character password from that set is 103 bits of entropy, roughly 11 orders of magnitude harder to crack than a password randomly selected from all typeable characters on a US keyboard but only 10 characters long (66 bits of entropy).
On the other hand, longer passwords can be more difficult to type manually (more places to make errors), especially when the characters are random, and also harder to memorize (much harder, for random characters even from a restricted set). So if people are likely to be manually entering these passwords, you may want to use (or at least offer) less-secure settings.
Also, even bad password policies can be pretty secure if the characters are chosen truly randomly. To take that Wells Fargo policy above, the maximum total entropy of their passwords was almost exactly 41.4 bits, which is a pittance compared to the other examples I gave but still impractical to brute-force over an Internet connection (on average, you'd need to make about 1.45 trillion attempts). That won't hold up to a determined local attacker, but would take a long time over the Internet even if the site didn't have any anti-brute-forcing protection. A typical human-generated (and easily human-memorable) password generated under those rules would be a lot less secure, though!