You can make a really nice burger with finely chopped fresh thyme (leaves, not stalks), seasoning, egg for binding and a grated onion, I add garlic too, but that’s up to you. Buy the best quality minced (ground) meat you can. I use my palm to judge the size of the burgers- if they’re smaller, they’re less likely to fall apart. You can try chilling them in the fridge for an hour or two- that should get them to hold together a little better.
If you’re willing to move away from burgers to other meat options, marinades are your friends. If you don’t want to up the cost, try chicken legs or wings.
Easy honey and mustard- honey, wholegrain mustard, a little olive oil and a dash or soy sauce, and that’s that!
Vary the quantities to suit your palate and the amount of meat you’re cooking. It’s especially good if you marinade some chicken breasts (fillets) in it, wrap them in foil and put them on to cook in their juices for a bit (you can finish them off over the coals without the foil if you want some colour).
Other good marinades- lemon juice, olive oil and rosemary is nice for white meats and poultry. If you don’t like rosemary, use thyme or another woody herb- if you use rosemary, you can even skewer the meat on the rosemary twigs.
Harissa works well with lamb, pork and chicken.
If you like barbequed fish, try wrapping it in foil with a simple herb butter.
You can make a good sticky BBQ sauce with tomato concentrate, molasses, honey or treacle, tabasco sauce and soy sauce.
Yakitori chicken is nice- mix mirin (or sweet white wine or sherry) with a little grated ginger, soy sauce, garlic, seasoning and a pinch of sugar (again vary quantities to suit your taste and the amount of meat)- marinade your chicken for an hour or two, thread onto skewers and BBQ, brushing with marinade every so often.
Also consider stuffing- if you’re doing steaks, lamb or pork chops or chicken breasts, cut the meat to form a little pocket (you can keep it closed with toothpicks) and stuff with whatever you think will be nice.
E.g.
Steak- peppercorns and fried onions
Chicken- mozzarella and sun-dried tomatoes; parma ham and parmesan; brie and bacon
Pork chops- sage, lemon juice and anchovies, apple (slices or sauce) and mustard
Lamb- garlic and rosemary
Anything acid will tenderise your meat- pineapple juice, vinegar, lemon juice, wine, whatever you like, you can use it as a marinade or brush it on during cooking.
If you’re really worried about cooking things properly, may I suggest an extra sacrificial burger- one you can cut into to have a look at the middle- it won’t change the taste, although it might be a little more dry, and you can always serve it to yourself (or one of the less fussy kids).