Considering what you intend, 1/4 aluminum should be strong enough. Certainly it will take the weight, and if you are not concerned about striking objects, you also don't need to be concerned about the bar taking a hit or bending if the jack takes a strike. For steel, probably anything 10ga or thicker is going to work (roughly 1/8 inch), and if flex on such a bar is also a concern, a perpendicular brace, say a half inch high, on the back of the bar would solve any flex issues. I really don't see a need to over-engineer the mounting bar, as the jack itself is quite stout, and so long as the quick fists hold, if the jack does not flex, the mounting bar won't either.
For what it is worth, I have carried a hi-lift jack bolted to the floor of my CJ-7 behind the front seats, for the past 6 years, and have used it exactly once. I find that it won't lift a tire off the ground on my Jeep without chaining the suspension to the frame, and on most surfaces, it is so unstable as to be useful only as a last resort. Seems that no matter how I block the tires, the vehicle always wants to roll off the jack, usually to the detriment of the sheet metal or someone's foot. I would never use one to get unstuck, as I believe that trying to use if for that purpose is just asking for broken bones. Since it is almost mandatory to find firm flat ground to use the jack safely, I find that once on firm ground, a small bottle jack under the axle tube or frame rail will lift the vehicle more reliably than the hi-lift, and in the past 9 years, all trail repairs on our club rides but one or two have been accomplished with a bottle jack instead of a hi-lift, even though nearly all of us carry the hi-lift as well. So, having it handy has never been high on my list of priorities.
