Options that I can see:
1) Same day morning flight, Nanchang to Shanghai Pudong arriving 09:30. I'd actually be personally comfortable doing this, since in the event of a major delay, there are Plan B flights---which go to Shanghai Hongqiao and requiring an annoying transfer to Pudong, but still with plenty of time to spare. Assuming flight is mostly on time, stick your checked bags at Left Luggage, keep valuables with you, and head to town for some sightseeing, food, etc.
2) Flight the night before. In this case, fly to Shanghai Hongqiao airport so you can dump stuff at a hotel and have some time for evening meal and lookaround, also next morning sightseeing before heading off to airport. No point in flying the day before to Pudong airport and staying out in that godforsaken wasteland, so your choices of flights the day before are more numerous than you think. This strategy is the most stress-free though likely more expensive due to Shanghai hotel cost.
3) D train--daytime departing morning--from Nanchang to Shanghai. I don't like this particular connection since these trains arrive at Hongqiao station. You have only one option, the D92 that arrives at 14:30, leaving you enough time but not a lot of cushion to get to Pudong. I personally see no advantage of this over the same-day plane, and would not do it.
4) Overnight train from Nanchang to Shanghai. The K288 and the K13 leave at 21:10 and 21:21 respectively, allowing for a full day and dinner in Nanchang. They arrive at 06:24 and 07:34 into Shanghai South station. K288 since it originates in Nanchang and is fastest, would be my pick. You'd need to park your luggage at Left Luggage then go to breakfast, sightsee, etc. for several hours before retrieving and taxiing to Pudong. Advantages are cheaper cost and your transport is your "hotel" and you'll definitely get to Shanghai with plenty of time to make your flight. Disadvantage is temporarily parking luggage in Shanghai and having to /retrieve, possibly not getting enough rest, and (since only regular soft sleepers not deluxe softs) less privacy. Getting sleeper tickets, depending on when you plan to travel, might or might not be an issue. Not a method all visitors will consider, but for balancing reliability, immunity to weather issues, and low cost, can't be beat,
Edited: 1:53 am, May 01, 2013