Could i grow in this? (DiY Hydroponic Garden)

Ok i am about to grow for the first time.

And i wanted a way that is small and can store somewhere.

Something that people wouldn't notice what it actually is ya know?

So i was looking and found this video on youtube.
The DiY Tutorial

And i was wondering if you got your plant to sprout if you can just put in in this, and grow it for the rest of the time.

Also i would like to know the best ways to start from the seed and some good fertilizer and watering tips.

And just as another quick note, i don't want to order things online so a lot of information on what to get from like local stores i.e. walmart/target/lowes. etc... would be great!