Is the gas grill an outdoor one ? If so, will the table live outdoors ? If so, then sooner or later it will get rained on and you don’t really want a solid timber shelf becoming a pond.
The time-consuming bit is doing the jointing. With a top and two shelves you’ll have 24 joints to sort out (one at each end of the horizontal pieces, if you like).
Pretty much what Jim said, but I’d use a pocket jig and screw it all together. You’ve essentially got two three rail ends joined by 6 longer rails. Make the whole lot from 50mm square timber. Order it online planed and square and cut to length. Buy a pocket jig, mark it out and away you go. Make the shelves out of decking as you say.
As for wood, Oak or Ash will do the job, use a strained preservative after, job done. Two hours work tops.
You have two legs at each end. On the width they are joined by three short rails, those are just the lengths of wood that join legs on a frame. I suggest you make those two ends first. Cut the legs to the same length then cramp them together and measure and Mark for the bottom and middle rail, you can then mark across all four legs at the same time.