Paying on your student loans will help as well. I agree with going the secured route now. The Capital One secured card is a good place to start. It is either $49 or $99 deposit with a $200 CL. Pay on that for 6-12 months keeping utilization low, and then you should be able to get a Cap1 unsecured card.
The only unsecured cards you could probably get right now are Credit One or First Premier. But their fees cost as much as the $99 deposit for the Cap1 secured card except they are recurring, which means they will have to be paid on a yearly basis versus a one time deposit for secured.
If you do decide to go with First Premier and/or Credit One, I would cancel their cards once you have been approved for better replacements. Once your score gets to 650-680 and you have at least a year of good payment history with no new baddies, doors will start to open up for you. Chase and AMEX are probably 2-3 years away but there are some in between cards such as Discover, Merrick, and Barclays.
I started my rebuilding with an unsecured Orchard Bank card. It really sucks that Capital One has took over the Orchard cards because they were the only unsecured cards available for really bad credit without the fees. All there was was a $59 AF. No fees for credit limit increases like Credit One and they gave frequent increases to their customers. Now that it is through Cap1, no one knows what type of Cap card it will become nor the credit requirements for it. Being that Cap1 has denied several members here a secured card with no credit or challenging credit, tells me that whatever card Orchard becomes, the underwriting requirements won't be as lenient as Orchard was. Cap1 is also stingy with increases and for most people, the only way to get an increase is to go through the executive office. And this is terrible because the only other unsecured cards available for credit profiles such as these are Credit One and First Premier and their fees take up 50%-75% of your credit limit which initially causes high utilization and that causes your score to drop much more than other new accounts do. So if you do decide to apply with one of them, pay those fees right away!
Good luck to you, you will get there. But I agree you want to start now. The more trade lines you have open reporting in good standing, the better...but only do what makes financial sense. If you are able to diversify them, your score will go up faster the more diversity you have. Like for me, I have a mortgage, auto lease, student loans, and 4 credit cards. Having all student loans and nothing else, stagnates your score. But only diversify if you need that type of credit. In other words, don't get an auto loan if you don't need it. Rebuilding is all about showing lenders you can manage the credit extended to you so they will extend more credit to you with better terms.