Hello blonder and welcome to the wonderful world of nappies.
Bucket - not too big or storage will be a pain and the temptation is to wait until it is full. You could use a wet bag instead as you could hang that out of reach of toddlers. They are attracted to them like a moth to a flame. You could just use a bowl in the bath or put them straight in the washer. Do not feel you have to buy a special bucket. I use a corner one from Ikea. It was about £3.
Mesh bag - I had one when I wet-pailed. I find them too much of a faff now, so do not bother. I use one to prevent baby socks and breast pads disappearing, but not for nappies. They are meant to make it less icky getting the soiled nappies into the machine. It doesnt bother me tbh.
Paper liners - hate them. Fleece washables (home made) are much nicer. If they say they are flushable, do not believe them. You will not need a liner with your choice of nappy, as one is sewn in. An additional liner could result in leaks.
Wet bag - this is something I am going to treat myself to. There are some lovely ones now. You can use plastic nappy bags, or a swim bag. You do not need a fancy one. May be best to wait until you know washables are for you, and that you still want DC in them out and about. I sometimes use disposables as I cannot be arsed carrying pooey nappies around.
Special detergent- not necessary IMO. Just use the value detergent and about 1/4 to 1/2 of the amount you would think you need. Do not use 2 in 1s or fabric softener.
Sanitizer- not necessary IMO and can damage some nappies.
Vinegar - never used it, but good for getting rid of smells. Only need it if you get a smelly batch, and it is cheap. The clear stuff. It goes in machine on rinse cycle I think.
Tea tree oil - I used to wet-pail in a soak of this years ago. Not recommended now. Some put a cotton wool ball taped to the lid of bucket to mask smell.
I wash every 1 to 2 days. No more than 3 days or smells will happen. I rinse out poos as soon as possible, then dry pail. I do not rinse wet nappies, just bung in bucket. I do a cold rinse cycle before a 40 degree wash. Some prefer a hotter wash, but I have never needed to do that. I do an extra rinse and an extra spin too. I hang outside, on radiators (not direct) or on maid as weather dictates. Your LL OSFAs will dry overnight pretty much. They do not need tumbling.
Keep your costs down as much as you can until you know if is for you. Do not feel you need to use them the second baby is born. Take time to get into a bit of a routine, establish feeding etc before putting added pressure on yourself.
If you need a holiday from them, have one. Both mine will be in disposables until I am recovered from my section.
If they do not work for you, do not feel bad (send them to me) as they are additional work.
Do join in on the nappy chat thread. But be warned, it can be addictive.
Once you know if you like them, you could think about washable wipes. They need not cost much either - you can buy swanky packs, but not necessary to. I have yet to get into them.
What colours did you get?