Hey there.
I'm not sure how long you'd take to clear customs, but I usually don't take longer than 15 minutes to get into arrivals. Then again I'm local so it might be different for you. If you take about half an hour you'd still be in rush hour methinks. Usually the jam is coming from the city at this time, don't know if it's the other way round (in the direction towards the city).
But anyway, here's my opinion regarding your three options:
1) Taxi: To the best of my knowledge, flag-down is $2.80, and since you're taking a cab from Changi Airport, there's an additional $5 surcharge. Also there's a peak hour surcharge from 5-8pm (35% or some percentage of total cab fare I think). This is your most expensive but most convenient option. Not sure about jam. We haven't even begun to account for the meter.
2) Airport shuttle is much cheaper if it's just $9. You should take that if it goes to or close to your hotel.
3) MRT. It'll be super duper crowded, especially when you make the transfers at Tanah Merah and Outram Park. If you don't mind the crowd (80% chance you'll not have a seat) and you don't mind that it takes about an hour and after that you still have to walk to your hotel, then this is the cheapest of the three options.
4) Here's another option. You can take a bus from the airport if you like (bus no. 36 from the bus terminal at the airport basement). You should be able to get a seat at least. To get to Clarke Quay MRT you'd have to transfer bus (to bus 195) at Esplanade though and total journey is about an hour. You'd still have to walk, but if you're trying to stinge every bit you can and you don't mind carrying luggage on a public bus you can try this. This is the route for your reference: http://gothere.sg/maps#q:changi%20airport%20to%20clarke%20quay%20mrt (click on By Bus instead of By Train + Bus)
Summary:
- Most convenient: Airport shuttle (if it brings you to your doorstep, if not then the taxi is next most convenient)
- Cheapest: Bus or MRT (bus gets my vote, you eventually get to sit down)
- Fastest: probably the Airport shuttle (if there's a jam everyone's stuck anyway, haha. But it's never that bad)
Hope you have a safe trip in Singapore. If you decide to pursue the bus route and need some more help, let me know.