Correct about DE, it's become standard to refer to all D-sub connectors as DB unfortunately, probably the fault of the early IBM PCs. If you look at the MAX3160 example schematic even they use "DB9" connectors
I like both methods, the MAX3160 is an expensive chip though, does that matter?
If you use screw terminals I'd use the plug/socket types as requiring a screwdriver to remove/replace wires is annoying and error prone.
If you use a D-sub connector people may have to solder up a cable, that's a pain as well.
Another option is to just use a 2x5 way header and use an IDC
DE9 connector. This also allows a neat way to mount the connector on a panel or enclosure side.