If you can manage it, and are digitally inclined, it’s nice to have something with a keyboard for fast processing in your “headquarters” as well as something portable that’s compatible. I know people who haul their laptops everywhere, but I think it’s not a great capture tool.
However, hardware and software will constrain your ability to implement and customize GTD. I have looked at many, many productivity apps and been impressed with only a few of them. My advice here is to go cheap and go simple until you understand better what you want. Microsoft Todo and Apple Reminders are workable and free, for example. The GTD setup guides can be very useful. I learned a lot from the original Outlook guide, and I have never used Outlook.