I have done a little reading up on WiFi security, and it appears that my 63-character random string is over-the-top from a usability point of view (although having set it up like that, I do not intend to change it any time soon).
A 256-bit encryption key is derived from the string (however long it is, 63 characters max) by convolving the string through a secure hashing process which uses the SSID string as a seed. Thus the string could be as short as you like, and the key would still be a 256-bit value unique to the string and the SSID.
However, hackers know the algorithm for deriving the key value, and have look-up tables of the SSIDs and passwords which correspond with particular keys - for common SSIDs and passwords. The SSID is recoverable from eaves-dropped WiFi traffic, so that just leaves the password. Hence your WiFi security depends on (a) not having a common SSID that appears on the lookup tables, and (b) not having a password that is common enough to appear on lookup tables - no matter how long (or short) the password string is. Thus with a personalised SSID and a memorable non-dictionary password string (eg "bLack%holE327") one should be as secure as my impossible-to-type-without-error randomly generated 63-character ASCII string.
All this depends on the WiFi network configuration being set to WPA2 (not WPA or WEP), and any WPS facility available on your router being switched off (which introduces an extra vulnerability through the 8 digit PIN).
Is it worthwhile hiding the SSID? Sometimes a hidden SSID makes inconveniences for the legitimate user, and a hidden SSID is no barrier to a determined hacker, but hiding it does make your network less attractive to a drive-by scrounger. I suggest hiding it unless it is inconvenient to hide it.