What do you think each crew member would have as their "everyday carry", like what they always have in their pockets or a bag if applicable?
Kaylee I think usually goes with pockets rather than bags, and I feel like she'd sew additional pockets onto her overalls. In them, you can find about 10 different types of multitools, various loose nuts, bolts, and screws, any flowers or shells or pretty rocks she and River gathered while planetside (she has dedicated pockets for each), a small romance novel, and some very sweet flavoured lip balm Inara gave her (not sure about the flavour, feel free to input!).
Wash, similarly, goes with pockets, usually in his vest, and they contain at least one small dinosaur ("for luck, Zoë, for luck! Imagine what could happen if I didn't have my lucky dinosaur!"), some kind of walkie talkie that connects to Serenity's comms system (there's no canon evidence for this as far as I can tell but I don't see why it wouldn't be a thing), a pen and small notebook (in case he needs to write down ideas for his dinosaur soap opera), the shells and rocks River and Kaylee have given him (also with dedicated pockets), and probably a fidget toy.
I think Inara has a range of handbags, purses, and clutches (to match her outfits, of course) that manage to have every item known to man in them despite their size, like that infinite bag from Mary Poppins or the TARDIS. Her absolute essentials would probably be a couple of cosmetic items (in case she needs to touch up), a pen and a small notebook (just for writing down things she needs to remember, really, but she enjoys doodling), a couple of choice tea bags, and, after working with Mal for long enough, a knife hidden in the handle of a comb (I realise I've made this sound like after working with him for long enough she's going to use the knife on him. I did mean for self defence from various criminal types but you know what maybe he should watch out), and one ornate rock and/or shell from River and Kaylee each.
If Simon were to carry a bag I think it would be like a satchel/messenger bag kind of thing, carried crossbody (this is me noticing that a lot of autistic/autistic coded characters and people (myself included) have crossbody satchels), and would mostly contain first aid supplies. But it would also have a pen and regular sized notebook (medical realisations, sketches of various things/people, his signature on the corner of every page...), obviously rocks and shells from River and Kaylee, probably a really fancy Swiss army knife or whatever the 26th century equivalent is (perhaps gifted from a grandfather, who died before River left for the Academy................. room for angst there), and either a Rubik's cube or a book of puzzles (in which case he would have a separate pen, specifically for the puzzles, and would refuse to fill them out in pencil).
Mal, simple as he is, uses only the pockets in his coat and does not carry much (other than his gun). A rock from River, a rock from Kaylee, and.... his cross. I don't know why I think he carries that with him I just think it's a neat idea. But it never leaves his pocket.
I like to think Zoë has pouches clipped onto her belt or something, because a lot of her clothes don't look like they have pockets (though she does canonically use her shirt in a pinch). She would also carry a small dinosaur (for luck, at Wash's insistence), the obligatory trinkets from River and Kaylee, a couple of spare credits, and some extra ammo. Prior to Simon joining the crew, she also carried a needle and thread.
Book mostly goes with pockets (something about it symbolising a lack of material possessions as opposed to a larger container like a bag), which contains some money and a pocket-sized bible. Also River and kaylee's shells - I think Book would pick the shells to symbolise the fragility of life.
Jayne actually wears cargo pants, so I think he's got some money (in case he stumbles upon a bar and/or a brothel) and bullets. Dedicated pockets for each type of bullet. The idea of him just having loose bullets is really funny to me, but that's probably also impractical. It took a LOT of needling from Kaylee and River to get him to keep the rocks in his pockets ("where are they sposed to go? I ain't changin' my system for some pebbles") but, of course, he acquiesced, and now keeps them in one of his hip pockets.
River mostly gives her stuff to Simon, since her dresses don't seem to have pockets, but when she's more independent she picks out a pattern for a nice crochet bag and some yarn she likes and sets out to make it. Along the way, she gets really frustrated that she can't pick it up as easily as she used to be able to learn new things, and Mal starts a crafting club so they can all struggle together. Participation is mandatory ("yes, Jayne, mandatory, unless you'd like a trip out the airlock") and no, he didn't do this because he cares. Of course he didn't. Simon and Kaylee's puppy dog eyes do not work on him (Kaylee has actual puppy dog eyes. Simon just kind of stares until Mal realises on his own what he should do. He learnt that from Book.)