In 1759 the chef for the Duke of Newcastle wrote a cookbook called A Complete System of Cookery and listed the utensils which every well-equipped kitchens of the well-do should have:
Stoves.
2 boilers, one to old a leg of mutton, the other two fowls.
A soup pot
Eight small stew-pans, of different sides, and their covers
Two very large [stew pans] and covers
A neat frying-pan
Two copper ladles, tinned
3 large copper spoons, tinned
2 Slices, tinned
An egg spoon, tinned
a pewter cullendar
4 sieves - one of lawn
5 copper cups, to hold above 1/4 of a pint
6 Do smaller
2 Etamines
3 large wooden spoons
Sauce pans, several
According to the book Georgian Cookery by Jennifer Stead, by 1700 the usual form of wrought iron fire basket (grate) was a large oblong basket on four legs, fastened to the chimney back with the tie bars, ideal for roasting large joints of meat. The spit rested on hooks on the two front legs and were usually turned mechanically by a clockwork spitjack, then later in the century by a smokejack sited inside the chimney and operated by the heat of the fire. The fire could be made smaller by winding adjustable sides or "cheeks" inward by a rack and pinion mechanism.
Stew and sauce making has been done over little chafing dishes of coarcoal on the floor of the hearth for a gentle heat.
(The book very helpfully included an illustration.)
From the late 17th century fashionable houses had a brick stove built into a corner of the kitchen under a window for ventilation. Let into the top were small round fire baskets, about the side of chafing dishes for charcoal. This arrangement would be much easier on the back as the stove would sit higher than a hearth.
Ovens were masonry and generally built into the thickness of the wall. They had to be laboriously heated by building a fire inside the oven itself, the sweeping hot ashes out and pitting the food to be cooked. The heat cannot be adjusted once the food was in. In the mid-century an iron oven with grate underneath (or a 'perpetual oven') was developed. It is often sited near the fireplace so it could share the flute and chimney.
The majority of people in the 1700's however cooked over open fire and didn't have ovens, They could roast meat but cannot bake anything. Instead they would send their food to be baked to their local baker and mark the food with initial. Some people might own a metal Dutch oven (it's not the same as the modern Dutch oven), it's a metal box with a front drop door and a polished tin interior to reflect the heat. It has a spit in the middle and it was possible to bake something on the bottom with the same heat. Thomas Turner, a Sussex shopkeeper wrote on Christmas Day 1756 they had among other things "a sirloin of beef roasted in the oven with a batter pudding under it".