Solid/sturdy is definitely key but I'm going to go counter to what some other have said. A vice doesn't have to be on a fixed bench, it just has to be sturdy enough to remain stable when working with it.
I pulled a fixture out of a scrap metal dumpster at a shop I normally buy scrap from. It's 20" x 24" and has a smooth/flat bottom with a very heavy (3x3x1/2 box tube) frame. I'm not sure what it weighs but it took 2 people to lift it in my truck. I'm guessing 200 lbs. I flipped it over, put casters on it, and mounted my heavy Yost vice on 1 corner to make a small mobile work table. That little table has proven invaluable. First off, my Yost vice is a pipe vice so it's taller than a machinist vice. Mounting it on a table that is about 24" tall has put it at an ideal height to clamp work and be able to get my body weight over it. The table is my mobile, cut, weld, and general metal working table. ETA, yesterday I had to do some welding on a livestock gate. I opened the shop door, pulled the gate in, rolled that bench over and clamped 1 end of the gate in the vice to hold it upright. If I have to work on long pieces of metal I can roll the bench/vice in any position I need.
One key importance that I think makes it stable is the casters are the type that locks the rotation of the swivel when locked, this keeps it very stable when locked. And weight is also important. A small table like mine wouldn't work if it wasn't so heavy.
I definitely wouldn't mount it on a toolbox...