Short version: information gathered from a variety of hanko shops (particularly Inkan Honpo, Hankoman, Hobundo, Hanko2510, and Shoyu-net calligraphy shop).
I’m quite happy with the quality of the seals I ordered from Inkan Honpo’s site, and their online preview not only gives you a pretty good idea how things will look in the different fonts, but also lets you set your own line breaks to improve the layout a bit. Their Illustrator templates for custom rubber seals are also simple and clear.
Long version:
Hanko 判子 and Inkan 印鑑 are the generic terms for signature stamps in Japan. The three round seals for individuals (Kojin-in 個人印) are for receiving packages (Mitome-in 認印), banking (Ginkou-in 銀行印), and officially signing documents (Jitsu-in 実印), but many people don’t bother with a full set. Corporate seals (Houjin-in 法人印) include the company name in the design as well as the employee’s full name, and there’s a round ginkou-in, a square signature seal (Kaku-in 角印), and a round official-document seal (Daihyousha-in 代表者印). The “artist’s chop” (Rakkan-in 落款印) is the other widely-seen type, typically square and carved as a negative so that the ink forms the background.
Mitome-in are the smallest (10.5-12mm) and most generic; if you have a common last name, you typically just buy one off the rack, and foreigners living in Japan will often just pick a random name. The primary constraint on size is the blanks on delivery forms, so 13.5mm is the practical limit.
Ginkou-in have a broader size range (12-16.5mm), with women preferring the smaller ones. Banks will let you register a signature instead of a seal, but they don’t really care what your seal says as long as it matches the one on file, so foreigners will often use premades for these as well.
Jitsu-in run a little bit larger (13.5-18mm), again with women preferring smaller sizes. These are officially registered with the government, so cheap rubber stamps are out, complex fonts are preferred for a bit of anti-forgery protection, and the name carved on the stamp must match what’s on your paperwork. This means that foreigners who want to use a katakana or kanji stamp must register that version of their last name, or else the stamp would have to be made in the latin alphabet.
Daihyousha-in usually run from 16.5-21mm, with the employee name or title in the inner circle and the company name running around the outer circle. Complex fonts are preferred, since these are issued by the company to say “this person who really does work for us signed off on the contract”, etc.
Kaku-in are typically 18-24mm, and can range from simple four-character designs to 20+ tiny little kanji recording the full details of company, title, and name.
Rakkan-in are whatever the individual artist thinks looks good. Commercially-made ones are usually square, but you can have them hand-carved in a number of shapes and sizes.
One cute little special-purpose seal is the 6x4mm oval Teisei-in 訂正印, used to initial corrections to a document.
An old-fashioned official seal is the Wari-in 割印, stamped across the edge of a document so that half of the complex design stays in the company’s records, so it can be matched up later to prove authenticity. The standard shape is a tall rectangle with rounded corners.
A variation on the daihyousha-in goes by the names Sensei-in 先生印, Shikaku-in 資格印, and Shoku-in 職印, and is used to show your qualifications. Round ones have your title/qualification (patent attorney, architect, etc) in the center column, with your last name to the right and your given name to the left. The less-formal square version has the title in the right column, your full name in the middle if it fits, and the two characters “之印” (“seal of”) in the left column. If you have a long name, you can skip the 之 or 之印 to make it fit.
Martial-arts instructors might use wari-in, square sensei-in, round jitsu-in, and/or kaku-in containing their dojo/system names. A Google image search for rank-test certificates will turn up examples with more than half a dozen different seals stamped on them.
One style that’s probably becoming rare is the Zousho-in 蔵書印, used for marking items as part of your library or collection. I’ve seen big ugly ones stamped onto old books and maps in ways that likely make modern archivists cry.
The ink is Shuniku 朱肉, with the color ranging from orange-red/vermilion/cinnabar to a rich deep “Chinese red”. The (relatively) quick-drying stamp pads are more practical, but traditionalists like Indei 印泥 (thick paste ink).
Now, what about the fonts?
Tensho 篆書 is perhaps the most common traditional font for everything except Jitsu-in and Wari-in, where the more complex Insou 印相 is preferred. Reisho 隷書 is still fairly traditional, but has the advantage of being a lot more readable; the characters are also relatively squat, which makes it easier to fit more of them into a seal without stretching/squeezing the shapes as much. Ko-in 古印 is popular among people who want to make a brand-new seal look old and worn, much the same way some people prefer stonewashed jeans or distressed furniture. Gyousho 行書 and Kaisho 楷書 are popular modern fonts, especially on rubber seals.
Sousho 草書 is pretty much only found on rubber seals, because the pseudo-calligraphy is hard to reproduce with engraving tools, and also harder to get a good impression with. Gothic ゴシック, Mincho 明朝, Souchou 宋朝, Seichou 清朝, Kyoukasho 教科書, and Kanteiryuu 勘亭流 are rare and also pretty much rubber-only.
If you don’t want the exact same digital font everyone else named Takahashi used, you can spring for Shokunin-bori 職人彫り (hand carving); this can be particularly useful for long or phonetically-spelled foreign names, where automated layout may be ugly. Hand carving is particularly useful for creating a space-filling design with Insou characters.
Some of the materials used for seals are pretty obvious, but others seem to be industry jargon that you’ll never find a description of outside of a hanko shop. Natural woods include Tsuge 柘 or Akane アカネ (assorted SE-asian “boxwood” varieties, generally the cheap stuff), Satsuma Honzuge 薩摩本柘 (Japanese boxwood), Kokutan 黒檀 (ebony), Byakudan 白檀 (sandalwood), Kaede 楓 (maple), and Ono-ore Kanba オノオレカンバ (Schmidt’s Birch, “axe-breaking birch”). Engineered woods include Saika 彩樺 (resin-impregnated birch, usually with natural coloring), Kurosaika 黒彩樺 (ditto, black finish), and Agni アグニ (ditto, red/brown-grain finish).
Suigyuuchou 水牛調 looks like it might be water buffalo horn, but is in fact just black acrylic used as a handle for rubber seals. Actual horn comes in Kurosuigyuu 黒水牛 (black water buffalo, dyed or natural), Sheephorn シープホーン, Oranda Suigyuu オランダ水牛 (Dutch water buffalo, with or without streaks of darker color), Manmosu マンモス (mammoth Ivory), Zouge 象牙 (elephant ivory, with appropriate certifications…), and possibly others. Kohaku 琥珀 (amber, possibly synthetic) is available, and Chitan チタン (titanium) seems to be trendy. Many places also offer quartz, Urushi 漆 (lacquerware), Hello Kitty, etc.
Stone seals are made from a bunch of different materials, mostly identified by where they were quarried. This calligraphy craft shop carries quite a few, in different shapes and sizes. (and now you know where I found the video of the Ink Pickpocket Boy…)