Are you planning on just building or are you planning on painting (and possibly weathering)? Bandai kits are really nice but the plastic they use is not typical to most kits so it will behave differently with paints, sanding, glues, etc. If you plan to just build it then the Bandai is great for a beginner, it a snap kit and will get you used to how parts go together.
If you want to get into fully painting then using any reputable brand will work. As Jakko mentioned, the Revell Star Wars kits are pretty good.
I havent built any Star Trek but Polar Lights and AMT seem to be the two biggest brands.