Stovies recipes vary depending on who you talk to and where in Scotland they live.
I live on the east coast and the tradition here is not to put meat in the stovies.
The way my granny makes them is to put beef dripping in the pan brown the onions lightly add potatoes and a little bit of water not a lot just enough to stop it from burning. then simmer until mushy.
Dh, who's from the west coast just makes mashed potatoes and adds fried onions and some corned beef.
My step mother, who was born in London but brought up in Scotland, makes hers in a pressure cooker. She layers potatoes, onions, carrots and lorne sausage until the pressure cooker is almost full. Adds a little bit of water then cooks it until it's all cooked(I don't have a pressure cooker so I'm not entirely sure about how much water/timings etc), then she mashes it all up.
All the above are really nice, in my opinion anyway. But there are so many different ways you should just try some out and see which one you like best.
Good Luck