Unfortunately, with those mortgage scores, you are going to have a VERY difficult time (likely impossible) qualifying for a mortgage within the next 6 months, even with money down. Lenders are going to see those scores as very risky. This is going to take some time. My wife and I also had to clean up our credit before we could buy our first home 13 years ago, but we got it done. It took us about a year and a half of very hard work, but we did it and were able to get our home. Give yourself at least another year of working on your credit and continue paying your bills on time. Definitely DO NOT miss any payments or be 30+ days late with anything because that can tank your scores in a heartbeat. You really need to let your credit accounts age. The lower the average age of your credit is, the lower your scores will be. Basically, the longer you've had these accounts open and in good standing, the more it will help your scores because it will show that you have maintained these accounts in good standing for a longer period of time.
If you have any collection accounts, you're going to need to start working on paying those off. Make a list of all the collections you have and start with the ones you know you can afford to take care of first. Then, contact the collectors and see if they will negotiate a smaller amount in exchange for deletion from your credit report. An important tip: When you contact these collectors, NEVER EVER admit that you own the debt. Just say something like, "I just noticed this collection account on my credit report and I need it to be removed. Can we negotiate a smaller amount in exchange for deletion?" Remember, these collection agencies buy these debts for literally pennies on the dollar and they don't make money if they don't get paid, so be firm and NEVER pay the full collection amount. If you have any older collections that are scheduled to fall off your report within a year or less, I wouldn't even bother with them. Why spend money you don't have to? Deal with the collections that still have a good bit of time before they expire and fall off your report (collections can stay on your credit report for up to 7 years).
Keep your credit utilization very low (preferrably around 10% or less). This is a big one, because credit utilization has a huge impact on your scores. You don't want to max out your credit cards, making it look like you rely on your cards and use them all the time. If you do use your credit cards, pay them off as quickly as possible (before the next billing cycle). Lastly, don't go and apply for a ton of credit. Keep those hard inquires off your reports, because too many of those can drop your score several points as well.
This is definitely going to take some time and hard work, so try to be realistic about how long it will take to get your credit and finances in good enough shape to qualify for a mortgage loan. There are so many factors that lenders look at when they are evaluating you for a mortgage. Your credit score is just one of the many things they take into consideration. They are going to look at your DTI (debt to income ratio - basically how much you make versus how much you owe), your income, any collection accounts, credit utilization, etc. Just keep plugging away at it as much as you can and I'm sure you will start seeing positive results.
PS: Why do you only want to buy under your name? Just because your husband makes less money and is self-employed doesn't mean that he can't go on the loan as well. In fact, if you add him to the loan and count his income in addition to yours, that will give you a higher household income and you can potentially qualify for more money. Self-employment still counts as long as he can prove his income and his credit is decent enough to go on the loan.
