Council tenancy or private rent would probably be the best idea. There are mortgages available for people with poor credit ratings, but the interest rates are quite high and if they are ever increased, you might get into trouble. Not a great idea, if you have new baby to look after, clothe, feed etc. You could look up independent mortgage brokers in your local Yellow Pages and then book to see them for a quick chat about what might be available at the moment. If there are high interest rate mortgages available, you can then work out whether this is likely to be affordable or not.
If you have any CCJ's on record, you may even have problems with private rentals, as letting agents will make checks.
Would suggest that you book to see your local councils housing people asap, as it may take awhile, for any suitable housing to be found. The government are looking to sell off more council housing at a discount, so if you are placed in council housing that you like and at some point are then in a position to buy, this may become an option for you.
After 6 years of debt being on on your credit record, they should come off automatically. Once they start to drop off your record and you reliably deal with all finances in the next few years, you will start to see your credit rating improve. Where ever, you move to, make sure you are on the electoral register as that will also help.