Korean BBQ comes in many varieties though it's always the same concept. You get a bunch of vegetables on the side, some strips of raw meat, and you cook and cut it up on your own grill. It's not the most creative food I've ever had but who cares, it's most people's favorite way to eat Korean.
BBQ is eaten with lettuce leaves, perilla leaves, bean sprouts, kim chi, garlic, onions and ten other things on the side. They each add their own dimension of taste, but I stay away from the Perilla leaf. The flavor is too strong to be eating unmarinated pork with. If you're lucky, you'll find a place where you serve yourself the vegetables because they are just as important as the meat. Carmelize the onions, brown the garlic and mushrooms, warm the kim chi and bean sprouts, then soak it all in the grease.
Most places have a wide selection of meats to choose from, domestic and imported from the US, Canada, or Australia. There is a difference in quality, but not as much as the difference in price- The cheapest cut is often half the price of the more expensive options.
There's nothing wrong with the cheap stuff, but as a rule it shouldn't go any lower than 2.5k per 100-140g.
The most common type of BBQ is Sam Gyup Sal. Thick strips of non-marinated, unsalted fatty pork. The quality and price varies considerably, but since it's pork it's going to be cheaper than beef.
My favorite BBQ meat is Duit-Go-Gi. I can't find any information about this online, but it translates to “back meat”. Jeon told me that it got this name because it's so good that butchers used to hide this meat in the back of their shops to save for themselves. It doesn't make much sense because what it actually is is meat from different parts of the pig near the joints, and it's cheap too- you can find it for 1.9k to 3k a serving. It's by no means a quality cut, but that doesn't stop it from being absolutely delicious. My best meal in Korea so far was at a The Original Gimhae Duit-Go-gi, across the street from another Gimhae Duit-go-gi in PNU.
PROTIP: There are two Gimhae Duit-go-gi restaurants on the same backalley on KSU's campus. They are good, but the third one is better. Good luck trying to find it.
A word of caution: There are places that sell Duit-Go-gi for 1.9k/serving. DGG is supposed to be served in chunks, not strips. I have not experienced this myself, but my friends have gotten some laughably shitty quality meat at that price, and even higher. I know this is counter-intuitive, but trust the Gimhae Duit-Go-Gi chain of restaurants if you want to be guaranteed a fantastic, cheap meal. Yes, it's a chain, no, it's not like Olive Garden.
Most BBQ restaurants are coal-fired. They will put a pot of hot coals in the center of the table and either a vented grill or wire mesh. The smoky flavor is nice if you don't mind a little carcinogens in your food. Some restaurants have Dr. Seuss tubes that extend from the ceiling, but they'll all have deodorizing spray bottles at the door for spraying your clothes down.
Personal Favorite: So Geum Gui (Salted pork) BBQ
This is the place I fell in love with. They use a gas grill with a tilted solid slab brushed in oil. The pork goes in the center so the fat can soak the bean sprouts and kim chi warming towards the bottom. You lose some smoky flavor, but not as much as you would switching between charcoal and gas with an American BBQ. And since its a slab and the meat isn't exposed to open flame, the tasty grease isn't lost.
What made me a regular at this place is the fact that the vegetables are free and self serve. I don't know how these people make any money at all, the cheapest cut of meat is So geum gui is 2.5k and the minimum order is 3 of them. That means you can bring like six Atkins-dieting motherfuckers, eat as much kim chi and vegetables as you want, and only order seven bucks worth of meat for the whole table. They pretty much encourage you to do so.
This restaurant is a clear triumph of quantity over quality. You can find it in Deokchon, from Exit 9, make a right, past Paris Baguette, and then a left. It's the first restaurant on the left, behind a small parking lot.