Glad your getting into throwing, its a relaxing thing to do once you accept it is going to take time.
I am going to probably be against the grain here but, I would actually advise against getting a lot of tools. Just get one rib, one wooden knife, and some fishing line or wire to cut pots in half/off bat.
I have so many tools that I bought that I thought would have been a great help, when in reality, I use 3 tools and nothing else now. The rest of the tools sit in a box.
1: a wooden knife, for trimming around the base while throwing / adding marks in my pots. / https://img0.etsysta...N.238958328.jpg
2: a rib : http://www.mudtools....v=7516fd43adaa-i use the yellow color, but if I was starting I would probably go with green. I like this rib the best, it has 3 points, a sharp corner, a dulled corner and a big sloping corner. It also has a flat side long, a flat side short, and a rounded side. I can make this rib do basically anything I need, smooth walls, make nice curves in bowls, etc etc.
3: a cows tongue (gyubera). I use this in so many ways I can't even describe it. The most useful thing I do with it is to smooth the bottoms of my cylinders and to align the bases of my pots so no cracks if I choose to dry them quickly. I also use it as a giant rib when throwing tall vertical forms.
3.5: a nice sponge. I say .5 on this one. I dont really use my sponge anymore. I just don't throw that wet that it is needed. Either way just get one really good sponge and it will last you for a few years. I spent like 8 bucks on mine and I still have it after 2 years and it shows no signs of tearing up. Course, like I said I dont use it a lot anymore
As far as bats and all the rest goes, just get a few of each type, you will find the one you like and stick with it forever. You won't need a lot of bats when your learning because most of the stuff your going to cut in half anyways. Maybe keep one pot a day just to compare to the next days ending pot.
For trimming tools just get the do-it-all tool by mud tools. It will get you by until you know enough about how you want to trim and what tools you want to use, then get a bison trimming tool. I love the bison tools because I can trim so aggressively. Most videos I see people pulling off little tiny amounts of clay with their dull tools. The bison tools I can rip off clay so fast, it's so worth the 70 dollars for the tool.
A chamois if you want to smooth your rims with it, you can just get this at walmart in a huge pack that will last you forever. If your throwing with a gritty stoneware, then dont use a chamois use a piece of plastic to smooth your rims, or do it like I do and thumb smooth manually after you trim them. Takes more time, but works way better and looks better imo.
Other than that I don't think you need anything else to get started. The less the better, focus on using your hands to get the results.
Good luck and post videos of your throwing!