Wasabi: The only powdered wasabi I know of that contains any significant amount of the real wasabi root comes from Penzey's Spices, and is not cheap, but you can order on-line. Everything else, powdered or paste, is green horseradish. Real wasabi root is delicate and expensive, and in very high demand. Most of the time wasabi in Japan is green horseradish too, though, so don't sweat it. (Although this does make a lot of the supposedly gourmet items containing "wasabi" a bit of a joke -- "wasabi mayonnaise" is just mayonnaise with green horseradish in it, but people will pay more for it because they think it's a gourmet item.) I personally would pass on buying root wasabi unless you know someone who really knows what he or she is talking about who assures you that it is actually of very good quality. In my experience, mediocre wasabi is worse than decent powdered/paste green horseradish, because it has almost no taste. I do prefer powdered to paste, because I find that the flavor degrades somewhat over time after you make up the paste; a lot of premade pastes include stabilizers and preservatives and stuff to overcome this, and I'm not a huge fan of those either.
Rice: I'm basically just passing on the standard wisdom among Tokyo-ite gourmet types, who get very wound up about the rice. You may have heard that a classic haute cuisine French place can be rated by the quality of its stock, demi-glace, and roast chicken. If those are perfect, everything else will be too. In a similar way, the quality of a sushi place can largely be determined by the nigiri: if the rice is perfect and the nigiri perfectly formed, everything else is bound to be perfect too -- you can trust the chef to season everything just so. In Kyoto, by contrast, the mark of a great chef is his dashi: if the dashi is perfect, you're in the hands of a master and can just let him take care of everything.
My suggestions about brands and types and methods are worth nothing. I don't like sushi rice -- never have. I used to have various ideas about why this might be, but after a year in Japan I discovered that it's just a taste thing: I don't like sushi. Now sashimi, on the other hand, is something about which I could write rhapsodies. My problem isn't the fish, it's the dang rice. Well, no matter -- you and it seems more or less everyone else like sushi, so go ahead. I'm just saying it's really, really important to get the rice right. But somebody else will have to make suggestions about the hows.
EDIT (forgot...)
Tuna: Tuna is normally cut across the grain, rather thick, in rectangular slices. The usual way to do this has to do with how you block the chunk of loin. Basically when you get it whole, it looks kind of like the letter P lying on its flat side, with the grain running perpendicular --- if you draw a letter P on a piece of paper, the primary grain of the fish runs in a line through the surface of the paper and down into your table, if you see what I mean. The object is to cut this into precisely rectangular blocks without disturbing the grain. So when you look at the block you've got, you've got to figure out how it aligned with the fish in its natural state. Cut the piece along the main line of the fish, i.e. parallel to the backbone and skin, so that the blocks you produce are rectangles (or as close as you can get) with one end exactly the size you want for your slices. Then you just cut slices off that end, working from the right to the left (assuming you're a righty), fairly thick, and you'll have perfect rectangles for your nigiri.
Sometimes, however, the end of your fish piece will be more of a triangle. In this case, you have to work out how best to get a clean rectangle out of this triangle. The remainder will be smaller triangle-ended strips. These you can slice at an angle into medium-thin triangles, or cut into long thin strips for making pencil-thin maki rolls (usually made with a small amount of rice and half or 2/3 of a nori sheet).
Of course, it all depends what you like. Sushi chefs are anxious not to waste any tuna, because it costs a fortune. For them, the idea is to get as much perfectly-blocked fish for slicing and putting on nigiri (or serving as sashimi), then after every by of that has been cut, to use some triangular parts sliced thin at an angle to make little sashimi rosettes. Then the remainder go into maki, where texture matters a lot less. If you prefer maki in the first place, that changes everything. Do you follow?
Edited by ChrisLehrer - 6/12/10 at 8:50am