Hi HSD, good moniker....
You have a success under your belt which means that you're on your way.
Screwdrivers, looking at what I use most I reckon you would benefit from either a 100 or a 120 (both if you can run to it), a 200, and a 300. As for sharpening them search eBay for "watchmakers screwdriver sharpener" for an inexpensive jig to help keep things true, and a fine grit oil stone of some description, failing that you can always use 600 grit wet or dry paper on a piece of glass.
For tweezers you might want to look out for a couple of Dumont No.5 or equivalent for hair spring work. Don't stint on quality here though.
For oils you would get a marked improvement with something a little lighter for your train wheel and balance pivots, Moebius 9010 or equivalent would be the obvious choice, this can also be used for pallet stones although not ideal. Also if you are likely to encounter automatics then a breaking grease for the main spring is an essential. Wars have been fought over the fine details of lubrication but I would be surprised if anyone would shoot me down over the above as at least a starting point. From there you can add almost as many refinements as you wish (and can afford).
M/S winders are a good idea if you can stretch to them, otherwise perfecting the art of hand installing springs can get you by, and an inexpensive crystal press will address most of your crystal needs.
But the big one (in my opinion) is regulation, and the ability to see what differences you have made. To that end having a TimeGrapher or suitable computer programme that can reliably show you amplitude, beat error, and rate, and give you a timing plot is a must for your wish list. This will allow you to see the difference between using Moebius 8000 and 9010 on the balance pivots, what happens when you over oil the pallet stones (or forget to altogether), whether or not the watch is in beat, etc. The list goes on.
I'm sure others will add to the above since everybody has their own ideas. But most of all just keep practising. The more you do it the better you will get.