Buying on price, I’d suggest the following selection criteria for tools (I know very little about Japanese knives, though I would speculate that the same principles likely apply):
1. Plain rather than decorative tools; the artistic finishes can add a lot to cost without making a tool any better from a functional standpoint. Tools that look unremarkable but cost more are more likely to be excellent quality from a standpoint of being able to take and hold an extremely sharp edge while being easy to sharpen and from a standpoint of avoiding any tendency to chip in use. The reasoning is that a smith can only command a higher price for a plain-looking tool if the quality will support the price; otherwise, customers will go elsewhere.
2. Hitachi White Paper steel #1 or #2, or Swedish steel. There are other options, but these appear to be the best for price/quality ratio.
According to what I have read, tamahagane (“sword steel”) can also be excellent and rival the Hitachi white steel, but the price for a particular quality level is higher. I have no personal experience with tamahagane, however, nor have I pursued any purchase of tamahagane chisels.
Blue steel, according to knowledgeable people with a great deal of experience (Stan Covington is one example), neither takes nor holds its edge as well as white, and is more effort to sharpen thanks to abrasion resistance from the chromium and tungsten carbides—doesn’t sound like my kind of chisel, so I never purchased any. I therefore have no personal experience with Hitachi blue steel, but I do very much like the white #1 and #2.
I put excellent-quality #1 slightly ahead of excellent-quality #2 based on my seven white #1 chisels purchased from Stan Covington, my three Koyamaichi white #2 chisels, and my one Iyoroi white #2 chisel. Clearly a limited sample size, so take that as you will.
From what I have read, the “Swedish steel” Japanese chisels are very similar metallurgically and performance-wise to Hitachi white, but again no personal experience.
I also have no experience with any “special alloy” chisels, nor do I have any knowledge of what the steel composition or in-use characteristics might be. I also have no knowledge about the price/quality ratio.
Unless you’re doing rough work that includes abrasives in the wood and possible nails, I’d also suggest avoiding the high speed steel chisels; again, no personal experience, but knowledgeable people with experience using such chisels seem to agree that they take quite a bit of extra effort to sharpen and don’t get as sharp (but will take abuse better, such as cutting through nails without taking major damage).
I hope this helps.