I suggest starting with a prototype made out of square tube and old bikes, especially if this is your first framebuilding project. Square tubing is a bit easier to work with (you spend less time mitring tubes) and the goal for the prototype is that it should be easy to build. Take shortcuts, in other words. Get something you can ride, then ride it. When things break, fix them.
As far as wall thickness, I'd buy whatever is cheapest. Weight for the prototype is not critical. For a final build in chrome-moly steel the thickness will depend on tubing size and how much stress it's under. You can buy plain gauge cold drawn 4130 steel tube in a range of sizes and wall thicknesses, usually by the metre. Which ones you want will depend on the detailed design.
Groups like Atomic Zombie and a lot of HPV and velomobile enthusiasts spend a lot of time just working this way, because it's cheap so you can afford to build things just for fun.
This site shows a steel prototype long john bike built and ridden, then eventually CroMo final bike built. There's some description of the design process and you can see the idea progress from welding random bits onto a steel chassis rail through to riding the finished bike.
One note of caution: you will need to tilt the pivot axle back from vertical to get more stability, but that design is inherently unstable.