If you are looking for a uniform fog in your scene, then you should just use a cube with a single density value in its volume shader. That will consume the least RAM, and is very quick to compute.
If you want variation in your fog, you can either create it procedurally in the shader editor, use a volume object (with an external vdb or with the mesh to volume modifier), or a fluid simulation set to gas. The simulation and vdb options are more likely to use more RAM, particularly at high resolution. For speed of rendering, procedurally generated density has the potential to be slower if the math is very complex.
Are you running out of VRAM, or is it rendering slowly? If it is slow, you can increase your Render Properties->Volumetrics->Tile Size. This will speed it up, but in general won’t look as nice. You’ll need to try each size and see which gives you acceptable results and speed. The Start and End values within Volumetrics are also very important. Ideally, you want the range between them to just barely enclose the volumes in your scene. If it is set to .1m - 100m, and all your volumes are between 2-4m from the camera, then you won’t see all the detail you have available; you may even see visible ‘layers’ in the volume.
Do you have a link to a post for the scene you are working on? You’ll get better responses if we can see the problems you’re having.
Here are some links to some of my scenes which use volumes of different types:
Pond in the forest and Leaf in a puddle use a simple cube with a uniform density (cycles).
Sunburst and Soft Gradient use a cube with a density which is controlled by a gradient, more dense at the bottom, and less dense at the top.
Cliffside pond uses procedurally created density variation (cycles).
Nebula is a complex shader, and I had to keep the render size small so it would fit in VRAM (eevee).
The conversation on Eevee cloud test is probably the most useful for you.