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, garrison cap... 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 or period sleeping bags... trust me it's 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 item 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
101st patches
wool Shirt
jump boots
trouser belt & suspenders
garrison cap
part 2... webbing & important bits
M1 helmet
Helmet net
helmet net scrim
webbing for rifleman
musette pack
m1936 pistol belt
m1936 suspenders
Carlisle pouch and tin
M1910/42 canteen cover
canteen & cup
rigger pouches
GP bag
1st aid pouch (tie on)
m5 rubberized gas mask bag
part 3... finishing off the webbing
mess tin
kfs (knife, fork & spoon)
entrenching tool (t handle or m43)
m1 garand bayonet
undershirt/vest (od or white)
m7 rubberized gas mask
shoulder pads
Part 4... more interesting bits
m1 Garand
pup tent (complete)
modern sleeping bag (only modern thing)
raincoat
greatcoat
wool jumper
gas brassard (it'll fall apart in seconds)
part 5... trinkets & decorations
dogtags
en bloc clips (to fill riggers)
bandolier (full)
British army bandage (502 had 1 each)
jeep cap
scarf (woollen or cut blanket)
part 6... the list goes on and on
wash roll
wash cloth
soap dish - soap
razor - mirror - shaving soap
toothbrush
period toothpaste (appearance)
1940s lighter
leather gloves
drop rope (I always have some)
k rations (not moral boxes)
d bars
Compass
thermals
part 7... the list goes on and on
Id (pay book, driving license etc)
pocket litter, period money etc
gas mask bag contents
French language guide
period watch
prophylactics
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
combination tool
lubricating oil (can)
bore cleaner (can)
cleaning patches
part 9... above and beyond
Mae west
t5 parachute
griswold bag
leg bag
c47
consumables
hexi fuel for cooking
matches / lighter fuel
food / snacks
blank ammunition
candles