Well, as the Huns you can get lucky and hit an upgrade ruin with your warrior. A Battering Ram can take a flatland capital solo in the early game, you just need to make sure that there aren't any enemy units around. On Emperor the AIs get a couple of warriors, but they usually send them away to clear a barb camp around turn 30, that's when you attack.
You need a production heavy start, look for horses and mining resources especially, because you can sell those early. Selling actually means declaring war on someone, waiting 5 turns and then trading the resource for a lump sum of gold in the peace deal. On Epic speed you can re-DoW them 15 turns later to get your resource back, either to sell it to someone else or keep it for happiness. It's a good idea to settle on a mining resource on a hill, because you don't even need to improve it then.
Try to get as much gold as you can. Move your armies in a way that allows you to demand tribute from City-States and clear barb camps. The Huns are particularly good at this, a single Battering Ram can demand tribute from any CS in the early game, except maybe a hostile militaristic CS on a hill. Hunting down barbarians also gives up to 30 XP to your units, and Horse Archers only need 60 XP to get Logistics.
Keep track of AIs' city count and take their expos in peace deals if you think your army is more than 15 turns away from that AI. This way the peace deal ends before your units get there and you have one less city to capture. Alternatively, use that city as a base to build/buy a new army.
Often it's useful to annex the enemy capitals instead of puppeting them. You can starve them to 1 population to minimize the unhappiness they generate, sell the useless buildings and get the useful ones, or just build/rush units. Be aware, however, that annexed cities increase the policy costs, while puppets don't. If you annex, get a monument in that city ASAP.
Get two armies quickly. To take the first capital, 3 range and 1 melee should be enough, but later you want both armies to have 4-6 range units, depending on the number of hill cities and enemy military strength. Tradition AIs' cities with a garrisoned archer can be a pain - steal their worker and use it as bait to lure the archer out.
Scout early and scout aggressively. Map knowledge helps you plan your attacks, ruins speed up the early game immensely, gold from meeting CSs is important, finding natural wonders helps with happiness, meeting AIs lets you DoW them etc. In this gauntlet I think it's a good idea to build a scout first, then rush buy another one while you're building a monument. Don't forget that you can use scouts as city capture units, they're actually quite good for that.
That's all I can think of right now... hope this helps! And my time has already been beaten actually.
Regarding the Great Musician, you can choose one from Liberty finisher. When you have zero tourism per turn, a Great Musician bomb has a default value of 150 tourism on Epic (67 on Quick, 100 Standard and 300 Marathon). The strategy is to have Greece as an opponent, eliminate a neighbour AI before they generate 150 total culture, and after that eliminate everyone else except Greece. Then as you finish Liberty and take a Musician, gift the first capital you captured to Alex and he'll (almost certainly) liberate it. GM-bomb the liberated AI and kill Greece. Now you're influential over the only AI in the game, thus winning a culture victory.
