If it's fairly good braising steak around 20/80-15/85 fat to meat content I'd use it for burgers and or meatballs.
UK butchers often sell two types by definition,braising steak and best braising steak,usually any sinew and gristle is removed but not always.
Best braising steak is often used for steak mince and makes great steak burgers.
The cheaper braising steak you might well find with the bone in.
I'm a sausage newbie too and beef sausages are on my to do list but burgers I've been making for years and for my next batch I plan to use a mixture of best braising and skirt,the price of skirt has gone silly though since more people discovered it.
For my last batch I used rump but that's only because it was on offer for less than even cheap braising steak and I'm not a fan of rump steak,it was poor quality meat,cut completely wrong,but I picked three good sized steaks with good marbling and fat and they made excellent burgers I could eat medium rare.
But I'd normally use best braising and any other decent bits I can get for burgers.
I mince once through a coarse blade and don't use any rusk/breadcrumbs.
Here's a recipe I've been using for years,not the only one but it works for me and makes a good burger.
I'd normally add some chopped smoked bacon as well but I wanted to eat these medium rare and this recipe was geared for a mate of mine who likes his McDonalds too much and wants to try making his own burgers so this is what I sent him.
1lb fresh steak mince
1 small grated/minced/or chopped onion
1 clove garlic(optional)minced/crushed or chopped,I find one clove works better with 2lb of meat if you don't like it too garlicky.
1 beef Oxo cube
1 egg(for binding)
1 dollop of good tomato ketchup or a squeeze of tomato puree.
Sea salt and black pepper
A sprinkle of dried parsley and chives.
Depending on your taste you can leave out everything except the beef,egg,and salt and pepper.
You don't desperately need the egg but it helps.
If you're going to mince the onion and garlic run it through the grinder last,it cleans out the last of the meat
It makes a lovely coarse textured burger that tastes like a steak and not that processed muck in the freezer cabinet in your local supermarket.
Many years ago(about 20 years ago)when I investigated buying a burger van a guy who made them took me a few doors down on the trading estate to the back of the factory where the burgers were made and showed me the big plastic bins full of gleaming white cows heads,the result of blowing all the nasty bits off and out of the skulls with a pressure hose to make burgers,there is no emoticon here for puke,I didn't,I have a strong stomach,but it would emphasise the point.
BM