Good advice from dray.
I've made sake with Calrose medium grain. It'll make decent sake. Nothing to brag about, but it's fine considering its relative cost.
The polished sake rice is much more expensive. But the milling removes the outermost layers of the endosperm where a majority of the proteins and lipids are concentrated. So if you're using unpolished rice you should do what you can to avoid any oxidation ... same as you would for your beer ... to avoid cloudiness (proteins) and sweat- or goat-like flavors from the lipids.
The "type" of grain (long, medium, or short) that we use is probably more important for us (homebrewers). As a general rule, long grain rice will have a higher amylose content than a medium grain rice, and a medium grain rice will have higher amylose content than a short grain rice. But there are exceptions to the rule – there are medium grain cultivars that have slightly lower amylose content than some of their short grain cousins (this is true of several California cultivars -- like Calrose).
So just avoid the long grain and extra long grain products. Basically, a high amylopectin (low amylose) content is preferred as it generally is more aborptive (water content) and more "digestible" for the Koji. The amylose-amylopectin ratio also affects pasting and gelatinization properties -- which is more of an issue for commercial use (rather than homebrew). But, there are some studies that show that sake made from low amylose rice tends to score better in taste tests.
As for the brown rice ... that's something I would probably skip unless you have a specific goal and really understand what you're trying to accomplish. Brown rice simply has the hull removed but retains the germ and some of the bran (so it's still brown). The good part is that bran contains about 60% of the grain's nutrients and the germ contains vitamins (thiamine, riboflavin, B6, E) -- all good stuff for yeast. The bad part is that the bran contains various oils (off flavors) and reduces the grain's ability to absorb water (protential problems for the Koji).
Anyway, sorry to be so long-winded. But with over 100,000 different varieties and well over 700 million tons of the stuff being used worldwide each year, the different products can make your head spin. It's no fun burning time & money on things that might be doomed from the start. So it helps to have some background on basic things that help.
Bottom line: try Calrose medium grain to start (it's inexpensive). Once you get the process down and have the appropriate equipment, maybe try some of that more expensive, highly polished sake rice. Then decide for yourself how much difference it makes.