I keep seeing conflicting answers on sites that give advise on how to best keep a rechargable battery. Pragmatically, the battery will die regardless of if you keep it plugged in constantly or not.
If you need a desktop solution, many mass produced PCs are relatively cheap, and you could go for one of those. There are a lot of barebones kits where the PC is about the size of 4 decks of cards. These would only need the unit itself, RAM, and storage.