The first step probably needs to be investing in a full set of credit reports and FICO scores for both of you. This may cost you $40 or so, but you need to have a clearly defined starting point, and be able to see detailed information on each and every item listed on both of your reports. Do not rely on scores from Credit Karma or anyone like that, those scores are useless. Credit Karma can be useful to help you monitor things like inquiries, collections appearing or disappearing, etc - but their scores are worthless.
Notice I said both - your lack of income doesn't help the approval, you're right, but you are starting in a higher score position, so if your score climbs along with his, you may be able to help with the interest rate that y'all ultimately get on the loan. His income, both credit scores for possible better interest/terms. You are married, so you can still apply alongside him even though you do not contribute income to the picture.
Once you know your definite starting place for each of you, you then make a plan.
Requesting a validation of a debt from a collector (or the original creditor) when you know the debt is yours really won't accomplish much. It may scare off some collection agencies (who will immediately close the collection and hand it back to the original creditor) but it won't make the debt go away. The original creditor can then either reassign it to another collector or write it off and 1099 your husband - either of which does not help. If the goal is to eliminate the reporting of derogatory information related to one of these old debts, PFD is a better option. Just know going in that getting a PFD agreement is not a sure thing, and in fact is not all that common - it just looks like it from the "success" stories you see all over this board. The reality is, there are far more "no go" results than successful ones with this. But it just costs stamps to try.
If you put a year into the efforts and still get nowhere on some of the old debts, once you hit a few months before they "die" (that is, before their 7-yr reporting life is up) you can try getting them excluded by the CRAs at that point.
Being an AU on your cards with good payment history and good utilization helps him - just like those things help you. Having at least one card of his own would help, but you need to be careful with inquiries and plan applications where you are reasonably certain of approval - in other words, he shouldn't be trying for a Chase Freedom or an American Express card with his scores as they are now. Capital One may be able to prequalify you/him/both for one of their rebuilder cards, or you might look at Discover IT secured or one of the other secured cards out there which graduate after a year or so of good behavior.
Getting late payments deleted by student loan people can be difficult. They are not supposed to delete anything, of course, and these guys are particularly hesitant to do so. Look at these as more of healing wounds - they may still be bleeding a little (hurting scores) but they will heal up and stop bleeding as time moves on. Even a year from now, their effect will be diminished from where it is now with no action at all. You can try to get them deleted with a letter-writing campaign, but there are probably other more definite benefits you can get out of your energy.
Do y'all own cars? If so, are they financed? If not, do you have any other installment accounts with a positive history (since your student loan records are not entirely positive)? If you do not, then you might want to look at a small personal loan from a credit union or other lender (I'm not talking about a title loan or a payday loan - avoid those! - but a small loan of a couple hundred dollars granted by a lender who'll let you make monthly payments over time to pay it off without charging you 642% interest). If you do have car notes, then pay those religiously on time. Building a better installment history can help outweigh the damage from the student loan issues as time passes.
Again, what you prioritize and what your long-term goals are will be determined by where you are starting on each file.
Pull good scores and complete reports, and figure out your budget so you know what cash you will have for settling old debts/collections while still keeping your utilization and your payments on your current accounts in good shape.
Make a list of the collections and chargeoffs with amounts, DOFDs, fall-off dates, potential for legal action (SOL dates), and who is reporting what (original creditor vs. collection agency) on both reports.
Come back when you have those answered, and we can give you more direct, detailed advice.
