Copper screen is what I've seen used for WLAN test
cages (strapped with copper bar and tied in multiple
places to good earth grounds).
Aluminum could be OK if you use that gray goop
(for service connection to breaker panel, etc.).
Tin sheet I think will be more expensive if you can
find it at all.
You might like a spectrum analyzer for assessing
whether any of the RF threats you imagine, are
present. Maybe a gain-block amplifier and an
assortment of antenna lengths for sensitivity.