Cheap XLR's will give you problems over time.
XLR's from major players (
Neutrik,
Switchcraft) will work problem free for years, especially if you choose the gold plated contacts.
I have many in my studio that have been patched to the same place for years and have no issues.
4 pin XLR's are quite common for 12vdc power connections on portable gear, typically wired pin 1 to gnd, pin 4 to +12v.
As mentioned,
Hirose and
LEMO are excellent connectors as well and are heavily used as interconnects in pro audio and on high end film/digital cameras.
They do take some patience to terminate.
Fischer are another robust, albeit pricy, option and are often found on older ARRI cameras and JL Fisher dollies.
Belden is somewhat of a standard for cable and Clark makes a
shielded DMX cable that might fit your application.
Generally the foil is left as close to the connector as possible, but only the drain wire is attached to the ground pin. Some people also choose to tie the ground pin to the shell contact present on some connectors so the metal housing becomes part of the shielding.
IMO, I'd go with the 5 pin XLR unless you fear there's a chance of your project being mixed into a lighting control environment and being confused for DMX, in which case you could use a 6 pin XLR and just leave one pin unterminated.