It's almost certainly not possible to get to anything like a single degree accuracy freehanding. Jon would tell you not to worry about it... especially on a knife as thin as the Gesshin Ginga. (He's told ME that, at least! And he never measures angles himself).
The Gesshin stones are relatively pricey -- though they are long-lasting for what they are, and they're bigger than many of the competing stones. The splash-and-go stones are less expensive than the soakers, but still, there are definitely stones that cost less that may be as good for your purposes, or you might like just as much or more. Those stones are very much to Jon's personal taste.
Before I bought anything from JKI, I bought a combination stone for cheap -- one of which is just "ok" from what I hear here (BDL has written of it-- it's the one from JCK, which I bought when I bought a gyuto from them, saving on postage and a stone, both). Jon at first discouraged me from buying anything else, just so you know... he thought it better than he'd expected, and that it was adequate for practicing on, and created a good edge. It's definitely nothing special, but nothing bad either; and finally the ability to sharpen, the technique, was more important than the quality of the stone.
That said, I worked on various of his stones, too (and bought a couple since); I like the Gesshin stones VERY much indeed. I worked on his 2000 soaker, which I thought was really great, and I may buy next. I asked about the Bester 1200, though, which is less expensive, and is part of the set of 3 sold for a very good price from CKTG. Jon said "great stone... I have a bunch of them myself, still". So there's that. I'd consider the set of 3 from CKTG -- it's a Beston 500, Bester 1200, and Suehiro Rika 5000 for a good price. Around $130 for the set.
Unless you've developed a taste for one stone over another, it probably makes more sense to go with the less expensive good ones just to start. (But then you might get obsessive and have to buy the Gesshin stones just so you feel like you 'know'... I don't know if you're one of those people or not!) I think often what people end up liking, at least for a while, is what they liked first. (Does that make sense?)
BDL has used a whole lot more stones than I -- as have various other people who post here. There are some threads already up that go into the question of "what stones should I buy?" already... so yeah, read about a bit. The Gesshin stones are pretty new to market, so you won't find a WHOLE lot of experience to read about with them; and especially not from people who have very broad experience and didn't just need a new stone after they came to market. On another knife forum, the 400 in particular got a LOT of praise as a coarse stone; but where you are in this journey isn't particularly needful of a coarse stone yet, and again the Beston 500 is considerably less expensive and highly regarded in these parts.
For one knowledgeable person's bottom-line set of recommendations -- Look at BDL's Post #14 on this thread: http://www.cheftalk.com/t/67301/mac-ultimate-v-zwillings-kramer-carbon-v-gyuto#post_362897 .
Edit -- I don't know when Jon will have the 240mm wa-GG back in stock, but he's in Japan at the moment, I'd be surprised if it's not soon upon returning. I did see, however, the 270mm is in stock. My preferred length, esp for a knife that light. (This is just me, maybe -- for me the pair of the 270mm gyuto and the 210mm petty works; the 240mm feels like a compromise, but maybe for someone who isn't enamored of the 210mm petty it makes more sense. I have the 240mm "surrounded"!)
Edited by Wagstaff - 9/26/11 at 10:05pm