The best propane grill is the one with the pilot that lights the charcoal.Dutchman makes a great point, something I know nothing about. But, my grill of choice for the past 15 years has been the Coleman Roadtrip, there are several models at different price points. Although this is a larger grill with its attached folding stand, it is a great stand-alone grill with plenty of room to cook almost any meal. I have a griddle top also with mine, they came standard back in 2008 with the grill, and now they are an optional piece, but I use it often for breakfast eggs, pancakes, and french toast.
You can't go wrong with the Weber models previously posted about. You also see many folks using Blackstone Griddles, maybe even becoming the most popular choice because they work great and come in several different sizes.
We also carry a small Weber charcoal grill because nothing beats steaks over charcoal.
I've done complete breakfast on mine, too, as well as burgers and such, but it has one drawback: uneven heating with its single burner, usually not a problem. Nonetheless it's a great addition to the toolkit, and I use it at home as well as in camp.It is just the two of us and the 17inch table top size is perfect.
Rather than wag that around, I suggest a $14 Butane torch which is compact, great for lighting campfires, charcoal grills, etc., and uses the same butane canister as this portable gas cook top which I consider an essential accessory for RV travel. You possibly can find the cook tops cheaper, plus the butane canisters, at almost any Asian grocery, such as Assi or H-mart or many of the smaller Asian stores.This is my pilot. If I wanted to cook on Propane I have a stove for that. I pack a small hibachi like charcoal grill & mesquite lump charcoal, and of course the pilot.