I like playing on lots of different maps. Every once in a while, I try to throw in a new map script or style. I don't like playing on the same settings for every game. It gets boring and my play never improves.
My favorite Warlords leader is Cyrus (Imp/Cha). For Vanilla, my favorite is probably Elizabeth. I usually choose a random leader, however.
I sometimes set Permanent Alliances, No City Razing, City Flipping After Capture, and Lock Modified Assets (if no mod is being used).
I play on either Prince or Monarch, depending on the desired challenge. On perceived "easy" maps, I will often play Monarch. I win fairly easily on Prince, but I have not yet become bored with it.
Small / Continents / Random Sea Level / Temperate - I find it easier to tolerate micromanagement when I don't need to obsess over every detail in a dozen cities. Continents keeps down the number of cities, as well. Also, with less competition, you will have a much easier time of founding religions and completing wonders. Clearing your continent of pesky AIs takes less units and less real-world time. All-in-all, it's probably a more relaxed and less difficult game. I usually go for the defaults, but five or six civilizations works well.
Medium / Continents / Random Sea Level / Random Climate - I often think of this as the 'default' SP game.
Large / Continents / Random Sea Level / Tropical - With more AIs comes more challenge. Tropical worlds are fun, because your cities often balloon to gigantic sizes. Expansive is marginally more helpful. Cottage spam becomes a potent strategy. Watch out for runaway AIs on their own continents. Mansa Musa sometimes launches spaceship parts while everyone else is bickering back and forth with sharp pieces of iron. Ten civilizations works well for me. This keeps the continents packed full of angry natives to conquer.
Huge Oasis - Ever played one of these? It's a crazy experience. I bribed Mao and Alex into attacking my worst enemies over a dozen times, each time with devastating effect. I didn't often need to get my own hands dirty, which was good -- I didn't have many strategic resources! After allying the world against a rogue nation several times, I eventually came to possess a wide-reaching empire with several close allies and a few mutual friends who were quite happy to vote me in as General Secretary. It was not difficult to trigger a diplomatic victory afterwards, after unifying the world against the people who refused to vote for me.
Large / Pangaea / Random Shore / Low Sea Level / Temperate - This is great for warmongering. Doesn't hurt for builder games, but the presence of so many nearby AIs usually leads to at least a couple major wars. The lack of naval combat doesn't really turn me off, but sometimes the over-reliance on melee units does lead to one-sided strategies. Warrior rush, axe rush, sword rush, mace rush, and maybe a final cavalry or tank rush. But I suppose it's still fun.
Large / Custom Continents / One Per Team / Random Sea Level / Temperate - My girlfriend and I play these often, with several AI teams vs us.
I also like Tectonics and Smart Map. Random, Shuffle, and Fractal generate good, random maps.