The buildings will be as beautiful in the night as during the day, maybe even better if still having the lights on them, and you can find some activity still in the red light district, but it will be the last little bit and depending on the weather it might have stopped before you make it to the city.
I would not bother getting into Amsterdam city, so little is open and what is open is likely not going to be geared to tourists around for a few hours only.
The one exception is that there might be clubs open, allowing you to dance (and modestly drink if you have a flight at the end of those hours) and get the athmosphere of the city: http://www.iamsterdam.com/en/visiting/whats-on/clubbing-nightlife-amsterdam or http://amsterdam.info/entertainment/ for places that might suit you and might be open.
There will not be many on a Monday night.
About transportation, that time of night the train is down to one per hour, (1:14, 2:00, 3:00 and so on,) and if you have just missed it you will lose about all the time you have to visit the city. So check the time and whether you can just catch a train, if not, taxi might be the best option.
Shared taxi or prebooked ride will be cheaper but might not quick enough in the short time you have. Most prebooked rides will combine different people to fill taxis or 9 people vans.
There might be a night bus, which is likely to run at different times to the train. The route planner OV9292 will help you find the best times for you.