Which visa?!

I am currently living and working in China teaching English on a Z, I have been here since March 2013 and my Z ends on the 22nd December, by which point I will be in England. I started doing an internship in September, which I am really enjoying, so much so, I handed in my notice to the teaching job, to go full time at the internship.

The internship will only pay me a 'subsidiary' not enough to be considered a salary. I am going back home for Christmas and I need to apply for a new visa. I am very confused as to which type I should apply for. L , M or Z? My internship can write me a letter of invitation but beyond that i'm not sure what they can do. I will be applying in my home country. I though M was best, then realised I will have to leave the country every 30 days which seems slightly ridiculous, as I won't have any money as i'm being paid enough to cover my rent. Any help would be appreciated...