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It's up to you about the $700 but I think it would help you.
If you shop at Walmart, that should be your first app. or some other store card that is backed by GE at a place you do shop.
GE will probably start you out with a small credit line at first but you can get a CLI every 4 months. You need to call them after every fourth statement closes for a CLI.
Then I would suggest either the Chase Freedom or the Bank of America 1-2-3 card. Both these cards will probably require HP for CLIs though.
Add two cards now and then hit the garden for at least 6 months before going for CLI on all your cards and then add another 2 cards.
Good luck!