Lancashire hotpot is a classic dish where I come from. Lamb, onion, potatoes, slow-cooked.
There's a short version of this post: Felicity Cloake's "perfect Lancashire hotpot" article in the Guardian is correct. Read that article.
Really the main way you can mess up Lancashire hotpot is by trying to fancy it up. As Cloake says, don't pre-cook the potatoes or the onions, or the meat. With the meat, lamb neck is a good choice, easy to find in supermarkets and good for slow cooking. (I bet Cloake is right that mutton is more traditional and would suit it well, but I don't tend to find that in the shops.) Cut the meat into BIG pieces - not "bite-size" pieces as in many stews, and not the bite-size pieces you get in supermarket ready-diced meat. Bigger than that. At least an inch thick.
I'm pretty sure I remember there being carrots in the regular school hotpot, so I add carrot (in big chunks so it stands up to the long cooking). Floury potatoes (not waxy) is the right way to do it, definitely - and for the reasons mentioned by Cloake: "the potatoes that have come into contact with the gravy dissolve into a rich, meaty mash, while those on top go crisp and golden â for which one needs a floury variety such as, indeed, a maris piper." I've got a standard recipe book here which says to put some potatoes on the bottom as well as the top, and that seems a bit odd at first glance but it gives you a good ratio of crispy potato to melted potato...
In a sense this is basically just a stew/casserole and you can do what you like, so I can try not to be too dogmatic, but it's one of those minimalist recipes where if you mess about with it too much you have "just another stew" rather than this particular flavour. It's traditional to use kidneys as well as meat (my grandma did that) but we didn't have that at school and certainly when I'm cooking just for me I'm not going to bother. However, I'm shocked to see Jane Horrocks suggest putting black pudding in underneath the potatoes! It's also mentioned by commenters on the Guardian article, so I assume it must be a habit in some bits of Lancashire... but not my bit.
That aside, the recipe to look at is Felicity Cloake's "perfect Lancashire hotpot" article in the Guardian.