Hi Gil, it sounds like the bumpy credit was 24+ months ago and so your credit history should be in good condition for FHA financing, you'll have more lending options (and easier underwriting) with the scores you are aiming for, but your scores now would also be OK (it looks like you got them from annualcreditreport.com or myfico.com - either place gives FICO scores which is what us mortgage lenders use). If all you have is the student loan & credit card debt (which you'd be paying off you say) then I don't imagine the student loan payments would get in the way from you qualifying for what you are looking at (unless the payments are like $1,500/mo - which I doubt). At a $150k sales price, 3.5% down payment, on an FHA loan including taxes/insurance/mortgage insurance, you could expect your total payment to be about $1,075/mo. You said you and your mom would be living there, there is a down payment assistance program called CalHFA, but it has household income limits - you can check more information on it at http://www.calhfa.ca.gov/homebuyer/index.htm
... overall you look to be in pretty good shape to qualify. I'd suggest you and your mom attend a first time homebuyer education course before though, it'll help you understand the homebuying & mortgage approval process and what to expect after you own your new home.