Hey!
I'll go on a different trend with omiyage. If you bring some, bring only for the important people. They don't expect it, but will be pleased and it always looks better (being a suck-up in Japan is a good point when you wanna ask something like vacations). If you are moving to the inaka (countryside), you will probably meet the town's mayor, might be in the local newspaper and such. I recommend bringing a little something to your supervisor at the BOE or school (ask your pred if you can... I gave something to my BOE supervisor and it helped get conversation going... all in Japanese I have to say). Don't feel obliged to bring anything though. If you have no room in your luggage, they will understand. Do bring things from home but leave the pamphlets behind, you won't use them AT ALL. Keaychains, flags, local team things are good for introduction or prizes if you are in a single school.. but if you go around, you won't start to give stuff everywhere. Basically, even if you do bring stuff, keep it low and don't bring too much. Omiyage in Japan is usually food and with the heat in August, they don't really expect you to bring anything since it'll melt/go bad.
About hygiene stuff. There are some things that you can get in Japan. When you learn about your placement, check if you'll have a Costco relatively close to you (less than 3hrs is considered reasonable...). Costco carry some stuff you might want in limited choice (speed stick deodorant for example). Also Tokyo has pharmacy called "American pharmacy" where they have some imported hygiene products too. Mostly American brands, like Bufferin, Advil, Johnson&Johnson, and Benadryl, as well as health and beauty products that may be hard to find such as the Burt’s Bees range.
http://www.sunnypages.jp/travel_guide/t ... y/1686/top Don't overpack, send stuff ahead and leave some room for when you learn where you'll be. My recommendation, if you wanna have winter clothes/gear, ship them. You can buy some in Japan but it isn't as warm usually (or size is a problem for some). Schools aren't heated in winter usually so most teachers work with a coat on and sometimes small gloves. Most JET houses are also old and cold so unless your pred tells you your house is nice and warm, think that it'll be as warm inside as it is outside in winter (check the average weather on internet and you'll get a good idea). For example, in Hokkaido I had to drain the water pipes before going to bed otherwise they could freeze and burst... But places like Hokkaido has a lot more facility in buying warmer clothes than say, Osaka. Like I said, it depends where you land. Ask around... pred, other JETs around there... get in touch with people.
Last thing, about videogames. There are many that you can here for cheap. Check out the forum on gaijingamers.com . They list the games that have both English and Japanese on them as well as trade and sell games for cheap. You can get many games for PS3 or Xbox from overseas that people brought with them as well as Japanese games... It's worth checking out once in a while.