I've never been to a track day where helmets are inspected (fnarr fnarr), but it's a good idea to get one that conforms to one of these standards:
SNELL SA95
SFI Foundation 31.1, 31.2
BS 6658 Type A/FR
These are acceptable for competition use, as are:
BS 6658-85 Type A (Type 'B' is not acceptable)
SNELL SA90
although the latter 2 may not be acceptable after this year.
If you're ever thinking of competing then you'll need a helmet with a visor or goggles in an open top car.
I've never been to a track day where fire extinguishers are anything more than advisory, although if the circuit isn't fully marshalled then it's definitely a good idea to carry a decent-sized one. A glovebox-sized handheld thing won't be much use. If you do carry a fire extinguisher make sure it is well secured, otherwise there's more chance of it coming loose and injuring you in an incident than there is of you catching fire.
Nothing else required for the FIA bar, but make sure you either have a head rest or you pad the cross brace on the bar very heavily.
Mike