Welcome to the forum @Martin_Thompson!
@wjcroft is extremely knowledgeable about neurofeedback, so my suggestions should be discarded if he has alternate advice.
As far as I've seen there's not really a consensus about the best multi-channel headset or amplifier to use. It depends a lot on your intended usage, technical comfort level, and budget.
From experience and what I've heard from first hand reports, I would say that:
Neurosky and Muse are the easy to use, inexpensive and allow data access, but have only a few, fixed-location channels;
Emotiv EPOC has 16 channels, but the saline electrodes make for questionable signal quality, and the data is unavailable unless you get the expensive developer version or work through this hack;
Pocket Neurobics devices are popular with professional neurofeedback practitioners and home trainers, so might be a good choice especially if you're looking at therapeutic applications;
- The OpenBCI has a lot of channels, provides good signal quality and data access, and is completely open source, but requires more technical proficiency to use and is somewhat cumbersome unless you get/make the Ultracortex headset for it.
If you're a programmer and thinking of developing software, I would take a look at the OpenBCI, with Ultracortex headset if budget permits. It is the only higher channel count device I'm aware of that's open source, and there's an active and helpful community that can answer OpenBCI-related questions.
For a general overview of affordable headsets and amplifiers, here's a neurotech hardware roundup post by @curiositry on our blog at Autodidacts.io. Also check out this NeuroBB thread about affordable neurofeedback hardware and software if you haven't already.
Good luck with your shopping! Once you've decided on a device, take a look at the NeuroBB Gear Swap category, and feel free to post a wanted ad.