I'm going to open with a caveat, It's been about 5 years since I lived in Honolulu, so my information is out of date, and might be incorrect.
First, if EMS is a career goal for you, then don't bother with WEMT, especially if you intend to stay on Oahu, there isn't any real wilderness on that island, if you're looking to move to one of the other islands, than it might be good to pick up, after you have your EMT.
Second, When I left, they were in the early stages of the process of basically doing away with basic, and making it I-99s and medics only, I don't know if that ever happened, but that might affect things.
Third, the place you want to be is working for the county, it at least was hard to get hired there when I was there, the other option for truck time is AMR, which is a little easier to get hired at., but still not fabulously easy. If I were trying to break into EMS on Oahu, after I had my license I'd go ahead and apply to the county and to AMR (Who knows, you might get lucky.), then I would start putting in apps to ERs. The big three you want to try for are Castle over in Kaneohe, Queens and the pink palace (I never spent any time up on the north shore, I think there's a decent hospital up that way you might try, if you live up that way.). If that fails, then you should drop an app to work in the ER at Kuakini or as a nurses assistant at Rehab (it's incredibly easy to get hired there, they have a hell of a turn over rate, and need ALOT of 1:1s). Once you have a job in healthcare, build experience and keep trying to move up the chain until you can get hired on at the county.