How are you, Mr. Genny.
The cheapest train from Beijing to Shanghai is 1461, which is also the lowest. It sets off at 11:57 and arives in Shanghai at 10:40 of the next day. The detailed price is below:
hard seat CNY88 soft seat CNY157
upper hard sleeper CNY176 upper soft sleeper CNY290
middle hard sleeper CNY183 lower soft sleeper CNY304
lower hard sleeper CNY190

From Shanghai to Guangzhou, you can take K511. It departs at 09:50 from the Shanghai South Railway Station and arrives at 06:42 in Guangzhou on next day. The price is as followed:

hard seat CNY203 soft seat CNY322
upper hard sleeper CNY345 upper soft sleeper CNY544
middle hard sleeper CNY357 lower soft sleeper CNY568
lower hard sleeper CNY369