I have experience with those burners and if you take a peek at my website, you'll see my advice is based on experience.
If you are a first time welder (assuming mig) use thicker material (1/8") and practice on scrap.
The stand will be too heavy but you won't poke as many holes in the metal from inexperience. There are some good YouTube videos on welding.
A metal chop saw will be all you need for cutting.
As for metal selection, go with rectangular mild steel tube 1" x 2" x 1/8". 2' x 2" is way overkill and adds weight without strength.
Take a look at how we mount our pumps, simple yet elegant.
You will need a 4-1/2" angle grinder, and a flex disc and many lots and lots of sanding discs. Harbor Freight is your best bet for consumables (NOT welding wire).
Do NOT use the frame as a gas manifold, this is not safe!
Look at lots of photos and draw lots of sketches. Think about where everything will sit and where all the fluids flow.
Oh, you better post photos.