I sometimes use stove for an electric cooker, but more in the context of put it on the stove. This is despite having a multi-fuel stove heating the lounge.
I'd say "hob" for the entire top of a cooker and "oven" for the bit you put food inside. You can buy separate electric or gas hobs to have inset in the worksurface.
Aga or Rayburn are both ranges, though Rayburn also make items purely for house heating - usually fires built into the wall with a back boiler that does hot water and central heating.
None of this is archaic.
Fuel was very expensive compared to what people were paid, except in coal mining districts where they were often paid in part in coal.
I remember reading an account of life in Aynhoe (called something like Apricot Village) at a period which might have been late 19th century or early 20th century. There was mention in there of how the village baker hired out his big oven on a Sunday for all the village to put their roast in - so they'd all trot along to the bakers with the joint of meat and vegetables in a metal tray, put it in a spot in the oven, go to church and collect their cooked dinner later. They were all doing moderately well to be able to afford to buy meat for roasting.
If you go back to 17th century economics, then the diet of the workers was pottage twice a day, or if you were slightly better off, porridge for one meal. Pottage was basically whatever you could lay your hands on boiled up in a pot.
Saw a documentary on Hannah Woolley a while back (cookery book writer) and she was writing in the Georgian period. The new middle classes had the money for some nice china and reasonable food, but mostly only knew how to cook pottage. So it was instructions for how to roast, or how to teach your maid to roast, cook cakes etc.
I'd go looking for websites by re-enactors - you get social history in that.
Further thought
Tea.
You want to check who could afford tea in 1829 if you are talking about tea imported from China or Ceylon. It became more affordable over the 19th century but I don't know enough to say when. Also look up mugs/cups/teapots etc.
Also - open fire. It is a hazard if you are wearing a long skirt, long apron. In 17th century it was one of the big causes of death of women, up there with child birth, as hems of skirts or aprons would catch in it. Closed stoves were a life saver. A fire up in a grate is less hazardous but not perfect.