I'm no expert but my lot love home made burgers so I make them fairly frequently, if you want thinner burgers just put less mix into your press just cause it's a quarter pound press doesn't mean that's the amount you need to put into it, if you weigh your burger balls,

before you press them you'll get a more consistent/uniform end product.
I sometimes press out a thin burger put a slice of cheese on it then press another one on top, instant cheese 'in' burgers kids love em.
Seasoning is important or they can taste quite bland, you need to experiment with various herbs spices etc to get the flavour you prefer, might get some not so great results but it's part of the experience bit like sausage making some strange sounding mixes actually taste pretty good.
I often add a small amount of pork into the mix to give it a higher fat content helps on the bbq to keep them moist, also try to make them in advance and then pop them in the fridge to chill them I've found this helps to keep their form and hold them together, as for the cooking indirect heat is better, if the burgers are right over the coals they will cook quickly and if your not right on top of them they can burn and dry out.
Buying pre-minced beef, pork, venison is more convenient but you can end up with small bits of bone or gristle so if I've got time I mince my own, small hand held mincer is all you need.
Have fun, happy munching.
Mark.