I had a pretty hard time getting it to the stage of manual review. The online team are completely useless at helping me get it approved. I ended up knowing someone who works in NAB and asked them if they can look into it further. After a few phone calls with many different levels of people it finally got put in for manual review. I'm anxiously awaiting an SMS.
During discussion I tried to justify my VEDA credit enquiries. They said, stop right there, we don't really need to know about why to be honest, we don't _necessarily_ look at that. So I'm guessing the main factors with Veda are that you haven't defaulted, no pay day loans, no risky $1k instant loans etc. And I'd say what they really look at is income - and your ability to pay it back (income/expenses). NAB have a really strict lending criteria, thus I wasn't approved on the spot... I guess they want to test the waters first, see how I go.
IMO the best option... Open a NAB bank account ($0/monthly fee) - put a couple $k in over the next few weeks, heck just pay rent out of it and transfer some surplus into savings. This will show them that you can manage finances and have some savings at least.
I'm trying this strategy now with Macquarie Bank for their HHonours Card as I hear Macquarie are pretty strict - will be interesting to see how it goes. It also doesn't hurt having $0 accounts with all the big banks as it makes applying for CC so much easier. This would also explain why Westpac offered me $19k with instant approval on the spot - no questions asked.