All of your "issues" will depend mostly on your budget, your current income and your savings. As well as your flexibility of neighborhood, location etc..
Two dogs to most landlords will be a bigger issue than a Bankruptcy. Make sure you have references for your dogs; that they are house broken, do not destroy property, are quiet even when you are not home, be willing to hire a dog walker etc. A vet reference to say that they are not aggressive etc.
This is not the best time of year for you to be looking because for every apartment at this time of the year in a decent location, priced right, they will have at least 6 applications!
This is the season for job relocation, grads moving to the City and college kids moving to the City to start college, so at all budget levels the rental market is the busiest of the whole year.
The smaller Landlords will probably be your best bet, rather than the large corporate landlords that have their formula and do not deviate for individual situations.
Best bet is to quickly analyze what neighborhoods are in your budget, find a good agent in that area and work with them.
Kathryn Lilly, Broker
Realty on the Greene, LLC