As far as i'm concerned you either start with some combination of wheel/agr/mining, or you don't. The other 3 techs are irrelivant to the point where you may as well be starting a tech down.
I'd add the caveat "and possibly fishing". If you have a water start, you can build a workboat first, especially if you have a forested hill or anything else that provides 2 or 3 production. It's an opening some players (far better than me, I might add), swear by.
Of course, there is no guarantee you get a coastal start. Unless you regenerate the map once or twice.
And I'm sorry to burst the bubble about china, but the starting techs are the *only* thing it has going. The UU below average at best, and the UB is just terrible. Even for a cultural victory, it's worse than having a leader with philosophical. It's a real shame china got stuck with 2 leaders with protective/+mediocre trait. Who builds archers anyway.
UU is definitely in top half, especially if you make an effort to beeline Machinery (after Writing, probably). It receives extra first strikes on top of the ones you get with Drill, has all the advantages of starting with Combat I (like unlocking Medic, Shock, and Cover), and the collateral damage means you can use them right after the catapults hit to continue the assault. On lower levels, you can usually use the Oracle to pop Metal Casting and get them even quicker.
I want to know how you survive without archery units--no longbows or crossbows?
Qin is pretyt powerful for a culture victory as he can wonderspam in three cities with the Industrious trait and has a UB that a UB that leverages it. Similar to Agustus and the Forum for an industrious leader.
Mao can expand a little faster being EXP and can defend the territory, but he is one of the weaker leaders.
I think Mao has the better of the two trait combos. If I'm playing for culture, I like Philosophical leaders like Pericles. As a matter of fact, I'd say Pericles beats out any other leader going for a culture victory.
Starting with "Agriculture and Fishing" are horrible unless you are creative.
How so? You can start with Mining -> Bronze Working, and either produce a worker if you have food resources or a workboat if you have a high production tile (if you like that approach). By the time either is finished, you will have Mining and can go on to BW.