The grill is the best addition to the galley when cooking aboard. Entire dinners can be prepared on it, and it uses minimal space and resources.
I recommend a good propane grill, such as Magma. The fuel source is easy to buy and store since it is in compact cans. If you have a dedicated propane locker, you can easily connect the grill to your large tank. If you don't, you can store your small camping size cans in a 4 inch PVC pipe on deck or in a well ventilated area.
I would caution away from using a charcoal grill because they are rather messy. When I was a kid, we used a charcoal grill. The food that came off of it was delicious, but the work involved with it was equally extravagant. The charcoal needs to flame up and burn down to embers, which can take a rather long time when you are hungry. After you finish grilling, you need to let it burn out and then dispose of all the ash. It can quickly become a very messy job on board a boat.
Another reason to avoid charcoal is the fuel source is rather large. A bag of charcoal takes up much more space than a small camping can of propane. If you were planning a long voyage, it would be very difficult to store and carry all those bags of charcoal. It would be much easier to store a bunch of small cans, and a lot cleaner too!
Lastly, an unconfirmed issue with charcoal deals with spontaneous ignition. Apparently salty charcoal can spontaneously ignite. I don't know if this is true or not, but I would not want to find out on board my own boat.
I would suggest splurging a bit when you buy the grill, there is a significant difference in build quality and longevity between the different tiers. I bought the Catalina Grill from Magma 2 years ago and it has been wonderful. It can get incredibly hot inside while not radiating heat outside. I set it on its legs in the cockpit (painted fiberglass) and the surrounding seat and backrest are cool to the touch. I have even used it during the snow, it cooked steaks beautifully and didn't melt the snow below or behind it.