There's no way any airline in this country is going to hire you straight out of school (unless you get into a cadetship programme like JetStar but that's a whole other story).
A degree is worthwhile but consider doing something other then an aviation degree. For instance an accounting qualification could land you a job with an aviation company and get you in that way. However you may wish to brush up on your english skills if you're going to do a uni degree
Parachute dropping usually requires 1000hrs minimum if they operate turbines. That's for insurance purposes.
As for small airlines you'll need to know what they fly and what rules those aircraft come under. If it's a light twin with 9 seats or less that's Part135 and you need 750hrs plus 50hrs on an IFR flight plan. If it's a Grand Caravan that's Part125 and they require 1200hrs!
Instructing is usually the most secure route here in NZ and if you do it through Massey they give their students first pick for instructing jobs (as do most other schools eg Ardmore, Bayflight etc).
Otherwise be prepared to leave the country. The Northern Territories in Australia, and Africa during the start of the summer season is a good place to look for jobs but you will need to be there in person (don't expect to get anywhere by emailing your CV).
I wish you all the best. Aviation is a tough nut to crack but it's worth all the headaches if you can stick it out.