I'm here to quickly break down to you the costs of your transport.
Travel Cards
Img Source: here
These paper cards are dispensed when you buy a standard ticket for a single trip.
It is commonly used by tourists and those silly enough to leave their cards at home. But did you know, this amazing paper card can be REUSED up to 6 times.
However, you have to constantly go to the top up machine and pay for your next trip.
Unlike the usual EZ-link card, which simply stores a sum of money for you to use up, you need to pay exact for each trip using this card.
When you buy a standard ticket for the first time, this card would be dispensed to you.
For the second trip using that same ticket, all you need to do is place that ticket on the card holder and then select your next trip.
This is the general ticketing machine! And long queue of people buying tickets
Convenience: 2/5
There are usually long queues at the General Ticketing Machines, and sometimes the machine would state that they are unable to give you sufficient change. Please read the screen carefully before inserting money!
Price: 5/5
You're not paying much more for the use of that paper card after all.
Ez-Link Cards
The common ones used by all locals.
Img Source: google search
From memory, such cards are purchased for $12. $5 for the card itself, $7 for its stored value.
If you are going to be heavily reliant on public transport (meaning at least 4 trips in a day), perhaps getting this card would be most convenient
Convenience: 4/5
You still have to queue at the GTMachines often, since you would top up only $10 at a time (the minimum amount for the adult card). Please note that the stored value in the card in non-refundable! You have to use it all up, or keep it for your next trip to Singapore.
Price: 3/5
I am not sure if $5 deposit that you pay for the card is worth that convenience, especially if you need one for every family member and if you are not travelling that often.
Singapore Tourist Pass
All the information you would need is found here.
http://ezlink.com.sg/singapore-tourist-pass.
Image source: the above site
I am not sure myself whether it is value-for-money, because it truly depends on how much you would spend on public transport.
If you stay at orchard road and only want to shop in the area, and maybe make a trip to the Singapore Zoo... then no, it is not worth it to get the pass.
If you are familiar with Singapore and would take buses up and down orchard road, or take the mrt to explore places like Chinatown, Tiong Bahru, Somerset and Marina Bay all within the same day, then perhaps it is a good idea to get that pass :)
IN CONCLUSION
Get someone else who has been to Singapore to lend you their card!
If not, the standard ticket/travel card/paper card should be sufficient for your travels :)
P.S If you're super hardworking, consider using this fare calculator to calculate your expenses!