When you say sausage, do you all eat it with bun like Hot Dog? Is it like a Brat here, or more of an indigenous sausage? I know the Bangor, but as I recall, it is more "Dinner Plate" type sausage, you know, with the mash and peas I believe. And I have heard of Lincolnshire, but I was lead to believe it was a sage based sausage and I always think of that as the breakfast category...America really has no sausage of its own...maybe a Texas Hot Link...
Regarding Lincolnshire, that is where I live, not necessarily what sausages I cook. For a breakfast sausage, I think I prefer Cumberland (shhhhhh, don't tell the neighbours) or even Lorne (square) sausage, which is what you can get in Scotland.
"Hot Dog" means so many things over here, and probably different things to different people. If you are having a hot dog from a van, or at a cinema, it will almost certainly be a frankfurter in a bun. I went off franks for a long while as most of the common brands over here are dirt cheap and contain mostly mechanically recovered meat, and even chicken (i.e. slurry). However, I have discovered some decent reliable brands that are proper meat, and beef and/or pork.
A hot dog cooked on the average british home BBQ will almost certainly be a variant on a British breakfast sausage, stuck in a bun. It is not quite right, but it is what we understand by the term, and can still be tasty. But to my taste, the British "banger" (sausage) has too much fat for this - it is fantastic on a plate with a breakfast (or - allowed to go cold, sliced and in a sandwich with sauce, it is wonderful), but in a hot-dog bun, it can tend to spray you as you bite into it.
So while I will serve those (and my friends like them), I do try to get Brats or similar when I can. They are not so available in our regular supermarkets as in the US, but some of the better ones stock them. However, it will never stop my friends turning up to my BBQ with a packet of British bangers!
I think the thing most in demand from my friends is pulled pork, which I have gotten quite good at cooking (for a Brit). Over the last couple of years, pulled pork has become a big thing in the shops - pulled pork sandwiches, potato chips etc; so when I tell first-timers that I am doing pulled pork, I often get a "yeah, ok" response, as if it isn't interesting food. Until they try my pork, and realise that what they sell in the shops is nothing like proper pulled pork!
With pork more or less under my belt (it can always be improved), I want to perfect my brisket. I've done it before, with both good and mediocre results, so I need to work on getting it consistent.