Some further clarifications
 

I believe that Jetstar still flies out of Terminal 1 at SIN (Changi). Just go to the airport web-site and look up the termininal.

Airport tax in Thailand is now 700 baht and collected in the cost of the ticket. Thai Air Asia is less than Bangkok Air, but beware of all the additional costs included when you get to the final cost of the ticket.

I agree Jetstar is the best option because it allows 20kg of baggage. It also assigns seats at check-in.

All of this is a pretty easy process once one decides what to do. All tickets can be booked on-line and paid with a credit card. All carriers use e-tickets.

Do beware that if you decide to use Bangkok Air on a Discovery Airpass, the process is more involved. Do a search for my trip reports on this.

Jetstar does indeed fly from Terminal 1 in SIN. At the moment the only airlines using the LCC terminal in SIN are Tiger Airways and Cebu Pacific.

A note about Jetstar that may apply to all of these LCCs being discussed:
Carry ons are STRICTLY limited to 7kg on Jetstar. They weigh it once at checkin, then before you are allowed to enter the immigration area, Jetstar pax are led to a different door in SIN than other airline pax... your carry on will be weighed again there. If you manage to get past those two points then you can pretty much get anything on the plane, they don't check again at the gate.

I did manage to cheat this system a little bit since I stayed in the transit hotel, I just left my carry on and computer bag in the hotel room when I went to check in (note, Jetstar does not have transit checkin, you must exit immigration and checkin at the regular checkin counter). So since my carry on items were not with me at checkin there was nothing for them to weigh. They said to me to make sure it wasn't over 7kg... just said ok with a smirk and went on my way. At the gate and on the plane not a word was said... so the trick is just to get past the check-in and boarding pass checking nazis in the departures area and you're home free.... :D