If you plan to go to Indonesia (Jakarta, Bali, Solo, Surabaya) or transfer domestically city to city, Garuda Airways (government's run) is the only airlines I can recommend. Beside bad track record, Garuda got better service and widespread counter across nationwide. It's easy to book while you were in Indonesia but not in the other part of the world.
The Garuda website only allow you to book so called e-ticket through this number 0804 1 807807 (Indo) or +62 21 2351 9999 (outside Indo) using credit card. You can do online transaction using Indonesia's banks (BCA and Mandiri), not within Garuda website. Again this made restrictions for people who not lives in Indonesia or having bank's account there. Indeed the e-tickets Garuda tends to give you above prices compare if you book direct in their offices.
When I used to live in Singapore, booking Garuda Aiways is a breeze using Zuji - a respectful online portal in Asia but rather expensive. Otherwise you contact Garuda representative near you. Sometimes the prices can be unbelievable sky rocketing due the season's demands. You will not get good bargain specially during Iedul Fitr and bank holidays.
Airasia is better known in Malaysia while it has links to Indonesia and several major cities. I have to admit that Airasia got better website which allow you to book online even though you were not in Indonesia. You can use any credit card , paid in local currency (including handling, sometimes airport tax separated) which make you easy to estimate how much in your host country currency. The price based on availability. There are few reports concerning delay of flight in Airasia Indonesia. That's the price you pay for low cost flight specially in Indonesia.
Airasia also based on localities. I can book in Singapore, Malaysia, or Indonesia's site with different currencies. I have been try Thailand's site but can not read Thai :) so yes their site is a global including payment system.
Only recently I discovered alternativeairlines.com -a site based in UK that allow you to book both virtually outside Garuda and Airasia. It does give you right amount but you will be charge addition fee £10 per ticket. For people who want less hassle, this site might be good for you. But for you in tight budget, I will recommend try above methods or connect with local Indonesian (count me..aha!) Once you inside the country you might be amazed how easy to book using travel agent or just pick the phone.
Oh did I mention Lion Air?