This height is known as "head height"

Good to know, thanx! :)

There are some hand pumps

Yep, but I am trying to make this a system that requires less parts, less maintenance and zero electricity. Not that I am an overly paranoid prepper or anything hehe ;) I just like the idea of this thing which is literally just a barrel, some valves and hose. Not much that will wear out and/or break too easily.

Thinking of the barrel/drum as a "reservoir" is a good point. The more weight I can create and the higher I can go with it, the better. I was thinking that if I stood the barrel up vertically and then welded a second vertical barrel to the top of that one would give me more psi at the outlet. Granted, it would take me longer to fill it up initially, but that (if I have everything sealed perfectly) should give me more pressure and hence more sucking power from the water source.

I know it seems a bit crazy to do it like this, but I think you see what I am going for here with the simplicity and sustainability of this thing. :)