Well, right away you seem to misunderstand terminology. Teaching English in Japan is a
foreign language (EFL), not a second language (ESL). ESL is what is taught in the US to foreigners.
GABA has not had a good reputation. I'd steer clear of them. You are on the cusp of the upper age limit for JET Programme, but consider it anyway. Their numbers have been falling recently, so maybe they'll ignore your age. Otherwise, big eikaiwas are a better route than GABA to get your foot in the door here. They will recruit from the States, and you will have to deal with their recruiting schedule and locations, but at least you don't have to pack a bag and live here first.
If you're coming to fund your travels, keep in mind that a job is a job, and you'll be expected to work when the company/school sets your schedule. With eikaiwas that might or might
not mean having Sat/Sun off, let alone 2 consecutive other days off. It's normal business here because those schedules cater to customers. If you go the ALT route through a recruiting company instead of JET, you'll probably not work on Sat/Sun, but the work conditions are different than in eikaiwa.
Beggars can't be choosers, and in Japan EFL teachers are beggars. The teaching market is in a glut right now, so you have to take almost anything you get. Children are getting more attention than adults for English education. I came at the same age as you and was very lucky that the eikaiwa which hired me had only adults as customers.
I'd suggest talking to teachers at the
ESL Cafe discussion site. Not many teachers on this one (I might be one of the few.)
Sorry, but you don't really have a choice in full-time vs part-time. It's full-time or nothing.
When do you want to be here? That also plays a factor in applications and interviews.