I’m a new griller, but so far I have bought:
Grill Grates.
A digital thermometer that you stick into the meat - it reads immediately and has really helped me with knowing when my steak and chicken was done. ETA: I just learned from gouf78 on the grill thread that these are called Thermapens. 
A special grill cleaning brush and spatula made to go specifically with the Grill Grates.
Several different planks that you can use for various meats. I had been familiar with cedar planks for salmon, but there are actually others you can use for chicken, pork, and beef.
My birthday is coming up, so I’m going to ask for one of those fancy thermometers that tells you how hot your grill is at any location on the grates (you can have hot and cold spots even with all burners turned on, and I would imagine if you are using charcoal as well).
I’m like one of those people who have just found a new religion or just started a new diet: very enthusiastic, but people are watching me with skepticism to see if I stay at it. 