Welcome to FT. I would recommend you explore EVA (BR) as suggested by other posters. Their economy deluxe product is excellent for longhaul travel at a good price. I'm not so sure about their FF program, you can check their website for details.

I've taken several trips on EVA, back when my discounted trips earned mileage on CO. Correction to my previous post: The CO OnePass program now offers miles for fares booked in C, Y & K classes, no more mileage accrual on J, M, Q, S, T, L, B, V, U, X, Z classes.

Transit to Jakarta is through Taipei. If you have a Diners Club credit card you have access to the EVA lounge, where you can spend layovers in more comfort. You can take a shower, etc., to me this is worth the annual card fee.

As previously mentioned, the cost difference between economy and deluxe economy on EVA is minimal, but the inflight comfort is absolutely worth the differential. There are numerous consolidators who provide good fares on EVA. I've used Borneo International in SFO several times for EVA tickets.