Prequals do not count towards a inquiry. Based on your scores, and being an AU already. Try Discover, they're pretty good for relatively thin files. Also might try NFCU since you have a Family connection. Amex is also another good choice. At least you have AU history as opposed to nothing at age 25, it could be next to impossible to aquire credit with no history.
As long as you don't have anything negative, just limited exposure. You should be fine.
Edit: I should also add, that you won't likely get high limit starting out. But it shouldn't take too long to grow them, Amex probably being the quickest.
Well...First off...Building credit is a marathon and not a sprint. It takes time to build good credit scores, a thick credit file and high credit limits. You have come to the right place to start your journey and the knowledgeable people here can make your journey as short as possible but I'm still talking years and not months.
Your best bet would be to try for your own NFCU card. You must have a connection to join because you already are an AU. NFCU is known to give some of the highest starting credit limits of all lenders.
You will need to app for 3 cards shortly. You will build a thicker file and be able to get the highest scores by having a minimum of 3 credit cards.
App for the NFCU card and stop back and let us know how it goes.
Hard pulls are the price we all have to pay to establish credit. As long as you are smart about it and don't waste hard pulls, there is nothing to worry about, the minimal damage they do to your score will disappear in a year if not sooner.
I agree 100% with @jamie. If I were you, I’d join NFCU first and apply for one of their cards.
Since your parents are NFCU members, you could join NFCU. They are relatively generous with starting limits.
If I were you I wouldn't use a personal card for business purchases, though, as that will create bookkeeping and accounting problems.
Its not a matter of which cards to obtain. It really is more about your attitude towards credit and debt.
Time, Patience, Perseverance and Tenacity are all components in acquiring high credit limits. You MUST pay your cards so that there is never ever a late payment. Always pay in full. You should strive to keep your credit profile absolutely flawless. If you fail to pay attention and ignore your credit responsibility you are doomed. The game requires your utmost attention to detail hence your tenacious drive to be ahead of payments etc. Slackers in the credit game usually foul out and then ride the bench. If you want to play and continue to score you must follow the card issuers rules. Time and patience will reward you with lots of the right cards with the right terms. Welcome to the game. It really is fun.