I would suggest you find some 40 or 41awg wire to start with. It's thicker so it won't break as easy. It's only usable with very strong magnets like a5 or ceramic as they don't yield many turns or a very high resistance. (Charlie christian pickups, El rayo, and a couple others) are made with thicker wire and strong magnets. Sort of in the grestch or rickenbacker territory as far as tones.
For your winding wire you can randomly find good deals on eBay but for the most part your best wire source is direct from remington. Most everyone else just resells wire they get from them so it'll be more expensive. They have a store on ebay and a website.
For strat and tele flatwork and rod or bar magnets it's hard to beat addictionfx, Dennis is great to work with and I think you can get slightly lower dealer pricing if you have a reverb store. I find he is also the best source for pole screws and slugs.
Tonekraft is the best quality flatwork in my opinion and they have good prices on flatwork and rod magnets, but they tend to take a month or so to fill your order. I normally have to call or email after a month to light a fire under them. Never had a problem otherwise though and he is your go to if you need custom made flatwork.
I used to use WD alot for covers and baseplates and screws and stuff, but their prices have more than doubled over the last couple years, even with a dealer discount.
Mojotone ebbs and flows on prices, also offer a dealer discount if you have a store. They have just about everything and are always the best source for bobbins. When I was last ordering supplies, I got most of my stuff from them and their prices on most supplies are pretty competitive to everyone else.
Philadelphialuthier is good for niche covers and if you need something quick as they normally ship within 24 hours, but they can be a bit pricey on most things you can find elsewhere.
I made my own winder and not sure if I'd recommend that for a beginner. But, you also may not want to invest a few hundred bucks on a legit winder to find out you can't get the hang of it.
For wax I think you can get by with a crock pot, I use a paraffin bath meant for hands/feet. Try to suspend the pickup if possible, don't just drop it to the bottom.
For a tensioner use your fingers
I find it best to sit the spool on the floor in front of me with my winder on a desk in front of me. To get the wire from the floor to the desk I run it through 2 pieces of felt tightened down with a c clamp on the edge of the desk, from there it runs through my fingers to the winder.
It's definitely trial and error to get a system that works for you. I personally hated the 2 sided tape method a lot of people use to mount the bobbin/etc with.
Make sure you have a good quality solder station too, no $5 Walmart irons. You need to adjust the temp if you're soldering a cover or getting hot enough to solder formvar or plain enamel.
A great idea to rewind pickups first and reuse those parts with maybe just buying some different magnets as most of the cheap stuff will be ceramic.
To magnetize rod magnets you'll need some strong neodymium/rare earth magnets. You can normally buy them magnetized but it makes assembly harder. It's normally best to buy your bar magnets pre magnetized as charging them with neos can be very inconsistent.
Make sure you tap your bobbins if using new stuff unless you want them to crack and split.
I wouldn't worry about counting your winds at first, just work on achieving a somewhat full bobbin. If you're off a few hundred turns on your humbucker bobbins you would call that a PAF
