Many people agree that the most important move to do at home is suburi. Suburi is a repetitive cutting exercise used in Kendo and in other martial arts. In Kendo there are many variations to suburi like joge-suburi, katate-suburi, haya-suburi and sayu-men-suburi. You should start with joge-suburi and do at least a 100 moving up to 300, 500 and so forth. Your personal mark is yours so try not to compare yourself to or envy other students. Soreness, numbness while practicing is inevitable so pay close attention to your body. The point of suburi is to loosen up the wrists and develop speed, endurance. Loose wrists are critical to proper technique as speed is crucial for, let's say, tsuki (we will devote an entire post to tsuki later).
Stay focused at all times as you might hit yourself, something or someone around you. People tend to damage ceilings, lamps and anything crossing their path. If you have low ceilings at home it is best to practice outside (lawn, yard, park, beach, forest) or in any place where you can raise sword properly without hurting technique. Time of practice depends on your personal mood and weather if doing it outside. However, be mindful about daily practice and choose same time of day for that.
The sword you use for suburi must be the heaviest one you have around the house. Between a 38 and 39 shinai please use the 39. If you have bokken or bokuto use them instead of shinai. If you can get a super heavy suburito, even better; alternate between bokken or bokuto and suburito. Many people don't buy, own suburito because of their sheer size and massiveness but believe me it is the best tool you can use to improve upper body strength. Save lighter carbon shinai for competition, it is not meant for standard home practice.
Finally, don't get discouraged easily, Kendo is hard and you know it! You should do your utmost to prepare “by the book” and demonstrate that you are worthy of Kendo. See you!