Everything... in order of usefulness and importance...
A lot of this will be obvious, for example the most important things is the M42 jumpsuit, then shirt, boots, helmet... at that point you look like a trooper. After that comes the webbing and weapons. Then what? What is most useful, what will you buy and never use and has no real practical function. Hopefully the list below will help some what. The only modern item listed is a sleeping bag, as much as it seems like a good idea sleeping in wool blankets of period sleeping bags... trust me its not worth it. You'll get no sleep and to what benefit? The public will have no idea you slept like that, you'll be cold, uncomfortable and miserable! Just hide that sleeping bag during the day under wool blankets or in a closed PUP tent. It is your only modern it that you should really bring as part of your kit. Even things like lighters and pens etc should all be period or period looking. There is no reason to have modern items in your pockets or on display.
part 1... the basics
M42 Uniform
wool Shirt
jump boots
M1 helmet + net
trouser belt or suspenders
part 2... webbing & weapons
firearm (m1 Garand, carbine etc)
m3 combat knife
m1936 pistol belt
role appropriate webbing (see 'your role')
musette pack
m1936 suspenders
Carlisle pouch and tin
M1910/42 canteen cover
canteen
cup
entrenching tool
part 3... (most useful non-essential items)
mess tin
kfs (knife, fork & spoon)
c-ration cooker (get it from me, free!)
any role appropriate items
pup tent (complete)
a modern sleeping bag (only modern thing)
coat (warm) - greatcoat or mackinaw
garrison cap
leather gloves
brown wool blankets (more the better)
wash roll
wash cloth
soap dish - soap
razor - mirror - shaving soap
toothbrush
period toothpaste (appearance)
Part 4...
jeep cap
scarf
wool jumper
1940s lighter
dogtags
spare canteen
m5 rubberized gas mask bag
m2 throat knife
tl-122-abc flashlight
part 5... trinkets & decorations
he grenades
Gammon Grenade
hawkins grenade
en bloc clips / mags for pouches
60mm mortar / .30 ammo belt
ammo boxes
A-class uniform
m7 gas mask
1st aid tie on pouch
drop rope (I always have some)
gas brassard (it'll fall apart in seconds)
part 7... the list goes on and on
bandolier (full of rubber clips)
Id (pay book, driving license etc)
pocket litter, period money etc
shoulder pads
googles / eye shields
gas mask bag contents
French language guide
period watch
prophylactics
British army bandage (502 had 1 each)
part 8... another bit of pointless kit
rifle cleaning kit, contents below
oil bottle
rifle grease pot (tiny)
m31 brush
pull through and brush
rubberized cleaning kit pouch
m3-a1 combination tool
lubricating oil (can)
bore cleaner (can)
cleaning patches
part 9... above and beyond
Mae west
t5 parachute
period wallet
griswold bag
leg bag
c47
consumables
hexi fuel for cooking
matches / lighter fuel
food / snacks
blank ammunition
candles