Thinking of buying a home in the later part of the year with a parent, though I would hypothetically only have about 3 months of work history. Is this feasible?

My family has never owned a home, and just recently my dad has decided that we finally deserve one. As much as I would love to buy a home and live somewhere I could call my own with my family, would it be feasible to actually buy one depending on our current circumstance?

My parents have never been good with money, especially my dad. Currently, they are not doing so well in the credit department because my dad was injured at work and was out for almost a year. Bills piled on and his credit took a hit. As of now, theyve been working on bringing down the credit cards ($4K+); I told them to pay off half of the balance every month until the balance is zero, not to pay it all at once. This will most likely be done with our tax returns and should be able to be covered by summer time.

The plan is to start looking around mid-july early august since his credit score would most likely recover to be around 700. He only makes about $42k a year (though he has been working alot of over time and could bump it up to almost $50K) but has been at this job for almost 6 years. As for me, I am currently finishing up my graduate degree and plan on getting a job in June (hoping for something around $50-60k; but conservatively $40k). My credit score is currently at 700 with no derogatory terms but I will be graduating with a total of $100k in loans.

Our plan was cosigning on a mortgage to have combined wages and credit scores to be able to afford a home we would want to live in as well as get the best mortgage interest rate. If its of any importance, we would like to buy a 2 unit so that we could live in one floor but rent out the second. What would be our options in buying a home, if any?