well, i wouldnt think safety is a big deal. otherwise the chinese government wouldnt worry abt the booming population then.
From Shanghai to Xiamen, your choices would be CHINA EASTERN, SHANGHAI AIRLINES, and XIAMEN AIRLINES.
I would take SHANGHAI AIRLINES, b/c it cares abt its customers more than the big 3 of china do. and lufthansa chose it as a partner in China to connect their customers, thus their safety record and service must meet their standards.
One thing you have to keep on mind that all chinese domestic flight's baggage allowance is 20 kg ONLY.
The other thing is that Shanghai has 2 airports, if you wanna connect to Xiamen the same day as your arrival in Shanghai you have to be very careful, since most domestic flights operate out of Shanghai depart at SHA not PVG.
Therefore if you wanna connect the same day, my suggestion is fly to PEK and then connect to XIAMEN, since all flights in Beijing are in the same airport, and Beijing got a lot airlines you can choose from. I would pick AIR CHINA if i'm in Beijing, and this might be easier for u as well, since you are connecting in the same airport, your 32 kg *2 baggage allowance will be extended to Xiamen.

Well, drop me a line if you have any other questions.