DHCP is simply a server task running, probably on your router, which hands out IP addresses to all machines connected to the network which have "obtain an address automatically" set.
I would normally say let it allocate a dynamic one as this way each machine should always get a unique address and you don't have to keep track of that. The server is doing that for you.
The time when you might want a static IP address is for devices that you need to connect into from one of the hosts on the network. Your printer might have a web-based management interface, for example. Tricky to find unless you know what IP address is on.
I guess the same might be true of the Humax box? Having said that, it might well come with software to manage it which will locate it on the network anyway.
"Always on" devices such as a set top box will generally keep the same DHCP-assigned address for a long period of time anyway, so one you've found it once, you should be able to remember the IP address.
What you must ensure is that any static IP addresses you assign are outside the range of IP addresses that the DHCP server is allocated as its' "pool" or you will get multiple devices sharing the same IP address, which is often fun.

Kevin