Keep the buds and short green branches on the trunk, these will be needed years down the road, and they are never replaced by the tree once you remove them.
Use the search function and read a number of Hinoki threads on this site. Do look up the Etsy wiring tutorial by Colin Lewis, it is free once you register.
Watering is tricky, looks simple, hard to get right. Use your finger, dig in to the first knuckle. If feels barely moist, time to water. Feels damp or wet, don't water. Feels bone dry, you should have watered yesterday. Get watering right, you won't have to repot right away. Watering frequency changes with the weather. Will also change as tree grows, or when you change potting media.
A coarse mineral based potting media (such as pumice) will last a long time, years to decades, without repotting, but will need careful attention to watering, daily in hot weather. An organic mix breaks down over time, often loosing air voids, becomes stagnant. Organic mixes need to be replaced every other to every 3 years. You should repot your tree in spring because the mix looks too heavily organic. Between now and spring read up on potting media.
You can remove any long branches you are sure you don't want. But keep the little ones on the trunk. Trust me.