Are you currently not training at all, or are you already doing other sports?
A punching bag at home is absolutely worth it if you want to train regularly. It's great for endurance, strength, and stress relief - and honestly, it's way more efficient than driving to a gym if you don't have the time for it. You don't even need technical knowledge; just hitting it and burning calories works fine too. Most cheap models (around 50-150 euros) hold up just fine if you hang them properly. The only thing that matters is that you have a stable ceiling anchor or a freestanding stand - a cheap plastic base won't do you any good, you're right about that.
For the basement you don't need much: a solid punching bag with a decent mount, maybe some gloves, and you're good to go. When it comes to installation, you should check if your ceiling can handle it (usually not a problem with concrete ceilings), otherwise get a stand. Cheap bags are totally fine for getting started; once you realize you're having fun with it, you can always upgrade later. Just don't forget that a bag like that also takes up space - there shouldn't be anything in the way around it so you can move freely.