|Some people advised to enable DHCP in the wireless router for a small range (outside the current DHCP range.) Which would be a better solution?|
Either will work. But it's simpler to use just one DHCP server. When the downstream router is correctly configured, it becomes transparent and all DHCP requests from wireless clients connecting to it pass through it to the DHCP server in the upstream router.
If you choose to have two DHCP servers running (not recommended) then yes, make sure the DHCP scopes do not overlap. You would want something like:
DHCP Scope = 192.168.0.100 to 192.168.0.150
DHCP Scope = 192.168.0.151 to 192.168.0.199
However, I'm a firm believe in the KISS principle when it comes to computing and having two separate DHCP servers running in one segment of a network is overcomplicating things. It also means extra configuration and just one more thing that can be configured wrong, or break.
I'm a networking professional and I'm telling you if I were doing this at home, I'd set it up with just one DHCP server and leave it at that. I suspect whomever told you to split the DHCP is not a professional like me because no professional I know would do it that way unless they had no other choice.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.