Two years after a Chapter 7 discharge, you can apply for an FHA loan.
You'll need to rebuild your credit to a minimum of 640, but you'll want it higher to get better rates.
Make sure tht you carry less than 1/3 of your credit limit per card, per month and pay more than the minimum. Always be on time. Make sure the car payments are on time.
As you know, your credit is evaluated in parts, not as a lump. It's the late payments that causes a drop. I have a client who missed 2 $40 payments, and his credit tanked 60 points. Ouch. Most lenders are more credit savvy than they were 5 years ago.
You mentioned that you could do an 80% LTV, but you'll only need 3.5% with FHA, and have some flexibility with closing costs. You wouldn't want to clear out your reserves, and it always looks better to the bank if you have a little cushion. Rates are so low that you wouldn't be gaining much by using up your reserves, but you do want to stay within a comfort zone on your monthly payments. As you well know, you could qualify for more than you would be comfortable paying every month.
Let me know if you need a little help, or L/Os who understand and work with credit.