I'm going to agree and disagree with the other posters.
If you're going straight from the airport to Disneyland, the train is definitely not the quickest option, and will take you halfway into Shanghai before going all the way out again. Having said that, I found the train easy and safe to use, and definitely cheap. It's not a scenic ride, but I liked that it gave me a little more insight into Shanghai since I didn't get much of a chance to see anything other than Disney. If you do decide to take the train, I would definitely concur with the posters who have recommended taking the Maglev from the airport. You will need to change trains at Longyang, and then once more after that. It is fairly easy to find your way between platforms, but be aware that you may not get working elevators/escalators at all stations and you may have to drag your luggage up/down a flight of stairs or two. On my first trip, I transferred to Disney from a hotel right near Longyang, and I could have sworn it took me closer to an hour than half an hour. However, I didn't actually time it, so it could have just been my imagination lol!
A taxi is definitely the quickest and 'easiest' option. Having said that, I'd read a lot about getting ripped off/scammed and/or lost, that I was terrified about taking one on my own, and thought the train would be the more reliable option. I felt much safer getting a taxi on my last trip when I was with a group of friends, and would probably even go for it as long as I had one other trusted person with me. If you do take a taxi, make sure you print off the hotel address in Mandarin, and it would probably be helpful to have some directions too. Have the hotel's phone number handy and a way to contact them (international roaming/local SIM etc) in case the driver gets completely lost and needs to be directed. Don't get lulled into a false sense of security thinking that everyone will know where Disneyland is. Pronunciation is different in Chinese, and the driver won't necessarily understand what you mean by Disney. And even if they do, they won't necessarily know where it is. Lots of people have taken a taxi with no issues, so I don't want to put you off, just want you to be prepared.
For the record, if I was doing another solo trip, I would take the train again. If I was with friends, I'd go for a taxi.