I am looking for a cheap and cheerful 360 degree camera to use as a hobbyist. What do people recommend?

If you are looking for something you can just use to shoot 4K equirectangular and upload, then the Nikon Keymission 360 is a good choice. However, you may not always be happy with the automatic stitch that it performs in the camera.
Also, in my tests, the rolling shutter is quite prevalent, and the frame rate is limited to 24fps, so don't plan on doing any fast action or using on a drone without a good stabilizer.

There are other cameras out there like Gear360 (requires Samsung phone) or Theta S, but there are new cameras coming to market like the Kodak Orbit 360 that could potentially be better with respect to dynamic range, resolution, frame rate. In the low-cost pro realm there is an interesting camera coming soon called the insta360 Pro.

Does the cheap come in here? What do you reckon the prices are for those?

The Theta, Kodak, Samsung and Nikon are all in the $300-500 USD range. The insta360 Pro will be around $3000 USD.

There are cheaper solutions that companies like insta360 have that can attach to smartphones, and I think those are in the $250-350 range, but the resolution is typically limited to 3K.

I use the Dual Kodak SP360 4K. Been a great system to learn 360 video, starting to get some paying gigs.

The Orbit is rumored to be released at beginning of March. From the specs, it looks like they listened to complaints about the Dual cams. The Orbit is one cam unit with two lenses (instead of back to back, no syncing issues and better stiching), will include EIS, better in low light, and will have a compatible gimble for additional cost.

I will be getting the Orbit, and would lean towards that over the Key or Theta. Apparently, there will be a pre-release discount for $100 off, making it $399.

actually, 180 3d will come and be better than 360 2d.
most of shooting hardly take adavantage of 360, and 360 makes very difficult camera movement.
if you want picture only , the theta-s is a great little tool. (unfortunately i break mine)
I use now Insta360 4k, because it is the only affordable 360 camera that can live stream 360 in 4k.

It doesn't get much cheaper than a LG 360 CAM. I pulled the trigger on one last week (it is selling for $129 on B&H and $119 on Amazon). You will still need a microSD card.

I bought it to dabble with 360 Video and it is really good value for the money. One cool feature this camera has is spatial audio. (Okay, it's a gimmick, and the sound quality is bad, but it shows the future) So when you view the movie via the Chrome web browser, the sound actually pans and tracks as one navigates within the movie.

I bought it to use with my iPhone. You don't need a mobile phone to shoot video or photos but you can't change the camera settings unless you are connected via their mobile app.

The raw files off the camera are unstitched (2 circles) but their 360 Cam Viewer desktop application will stitch and make the files ready for uploading or editing after using the Google Spatial Media Metadata Injector tool on the files.

It is an interesting workflow and when viewed via my ViewMaster VR (Google Cardboard) viewer...it's frighteningly "real".

+1 to the LG 360 Cam. Super cheap, really good form factor, and surprisingly good picture/video quality. Not quite on the Samsung level but also 1/3-1/4 of the price.

I think I got one for $80 used on ebay