In this vein, you’re going to need to get one of these. In my experience, it’s just too darn hard to balance a bird on just a can and its legs - this simplifies everything so you can focus on your own beer can. Shove a couple lemon wedges, a few sprigs of parsley, cilantro and/or basil up its butt first, rub it with salt and pepper, set the grill on low, and you’re good to go.
Nuh-uh! 
I’m just the opposite. The Weber sits in the corner, covered in spider webs, while the propane grill gets used multiple times a week.
Marinades are something else to explore, as others have mentioned.
I’m not totally anti-propane. It’s great for the convenience factor, I suppose, but I like making fires, I like the taste of real charcoal and wood, and nothing will ever beat grilling the way our ancestors did. Live coals will always rule my world.
Anyhow, on a related note, for tips on grilling a great cheeseburger, the OP might want to check this video out. Pretty much my exact burger philosophy (except I tend to go for 80-20 chuck rather than 85-15.) Actual grilling tips start at 3:20. The part before is meat selection, and the part after is some rather absurd monstrosity of a burger that looks intriguing, but also like death on a plate.
edit: Oh, and in the Gary Wiviott book mentioned in that video, the basic dry rub recipe he recommends is 2 parts salt, 1 part paprika, 1 part black pepper, and 1 part herbs & spices of your choice.
So, why not just use the broiler under the stove? 
Let’s see…bend over every couple of minutes to check food in broiler, while getting in the way of the wife who is trying to get her half of the meal prepped, or stand upright on the patio with a beer, enjoying the breeze and the cats? Which to choose, which to choose? 
Burgers: onion salt and black pepper. That’s all. Anything else is mere frippery that makes your burger cease to taste like a burger and begin to taste like a steak.
Steak: my personal favorite is Great American Land & Cattle Company seasoning, but feel free to experiment. Whatever you choose, oil your steak up first, sprinkle the spice on heavily, and pat it on to help it adhere better. You’ll still lose a lot to the grill, but more will stick.
Chicken: lately I’ve had good luck with Grill Mates marinades, which come as a spice mixture in a little pouch that you mix with water, oil, and vinegar. Marinate your chicken in it for 15 minutes (more for better flavor) and grill, basting with leftover marinade if you like (I like). The “Baja Citrus” is particularly good.
I see your point.
I don’t think you understand. This is it. This is the mastery of steak making. But I forgot one thing. Douse the steak in Dale’s. It’ll be near the barbecue sauces and marinades in your grocery store. Douse it first, add the Roasted Garlic and Herb, Montreal Steak and Season-All (you can use the spicy variety if you like spicy things, I do) on both sides, stick it in a freezer bag and put it in your fridge for a bit to marinate the steaks. I do it on propane all the time and once you try it you will understand.
Don’t overlook marinades. My current favorite for chicken breasts is the juice of two limes, two tablespoons of ground cumin, two tablespoon of garlic powder and a teaspoon of salt. Marinade for a half hour, then grill.
Flank steak, I hope. If you’re putting Dale’s on a good cut of beef, you’re doing it wrong.
Another method of grilling not mentioned yet is wet grilling. I use a an old cake pan I picked up at a garage sale, an aluminum cake pan from the store will work. Don’t use your wife’s good cake pan, this will ruin it. Get your coals nice and hot, make a hold in the middle and set the pan in. Spread the coals out around the pan, get some up next to it. Fill with a flavorful juice or liquid, my faves are pineapple juice or V-8. Put your grill in place then place your meat over the pan of liquid. This is an indirect method of cooking and will take about twice as long as cooking directly over the coals. Resist the temptation to keep checking on the meat, it can’t burn using this method. I put the lid on and wait up to an hour before checking the meat. This can also be done on a gas grill, just keep an eye on the liquid. Add more if it runs low. The meat will come out very juicy and with a hint of flavor from the juice. Flank steak and London broil are the best cuts to cook this way. I have also used beer, wine, pomegranite and mango juice.
As far as seasoning goes, if you can get it, Johnny’s Seasoning saltis the best.
We made a mighty fine one the other night with (forgot the proportions, sorry): lime juice, soy sauce, minced ginger, and apricot jam. Whisk together, let chicken soak, baste with the extra…MMM on the grill.