No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I have been told by every mortgage broker that I have worked with that FHA will not finance you if you have federal student loans in default. Their perspective is, "if you defaulted once on federal money, what is to say you will not default again".
Now, if you go to the mortgage thread, you may read otherwise from time to time. However, a signficant determining factor isn't what you read on the message boards, but how the broker & underwriters interpret that.
In closing--you said you wanted to buy within 6 months--an extra three months on top of the 6 & you will have completely rehabbed loans.
Good luck!