IT all depends upon how close to something that might have existed back in your chosen time period you wish to achieve.
The simple answer is 6 to 12 inches cut off of an old oil drum, with some method of attaching legs to raise it up high enough - and then a bag of sand to pour inside it to build your fire on. It's light, simple, easy to replace. Looks like sh*t, but it meets the requirements and works. Some people use a truck/semi brake drum for the base, with steel plates bolted/welded in to seal up the bottom.
Those square braziers are documented correct from the mid 1800's on back to the Middle Ages. And there are round versions. But you still have to put it up on something - so the heat from the bottom doesn't scorch the grass/ground. I usually carry along several fire bricks. I lay them out on the ground (or on a table) and then put my brazier on top of them. Some people have had a metal table/bench made up just to set their brazier(s) on, and raise them up high enough. The stands are kind of hard to document, but they work and they meet the fire code requirements.
One big/heavy option would be to make a "raised hearth" out of wood/iron, brick, and sand. Make a wood or iron framework, then layer in fire brick/sand to build your fire on. Think of it kind of like a blacksmith forge without the attached bellows. Versions of these were used on ships all the time. Some were built right down on the deck/floor, and some were raised above it with firewood storage below. You just need enough brick, mud, sand to insulate the wood from the fire. And it raises the cooking fire up for easier working around.
So, it's all a matter of how far you wish to go. Just don't drag along that tin/aluminum BBQ grill on wheels! (unless you have no other options)
Just a few humble thoughts to share. Take them as such.
Mikey - out in the Hinterlands