1/ luggage
Compared with westerners, who often travel with large suitcases, it's not common for Japanese people to travel with a large suitcase around the country. Consequently, there isn't usually a wide space to store large luggage in trains, and the coin lockers aren't large enough to hold them either. Keeping your luggage small is recommended when you travel around Japan. You might want to bring several small bags so that you don't have to carry a large suitcase.

2/ Shoes
Since it's a Japanese custom to take off your shoes indoors, you might have to take off your shoes often in Japan. Bringing a pair of shoes that you can slip off and on easily might be convenient. Make sure to bring, and wear, a nice pair of socks or pantyhose to avoid any embarrassment when you take off your shoes.

3/ The weather in March is:

City Average Max. Temp Average Min. Temp. Rainfall
Sapporo 38 F (4 C) 26 F (-4 C) 3.1 in (80 mm)
Tokyo 55 F (13 C) 41 F (5 C) 4.5 in (115 mm)
Osaka 58 F (13 C) 41 F (5 C) 3.9 in (100 mm)
Fukuoka 57 F (14 C) 43 F (6 C) 4.3 in (109 mm)