I would not pay any type of deposit, until after signing a lease. Things can fall through and you don't want to lose any more. As long as you pay the pet deposit before the pet enters the home you should be just fine!... more
The bankruptcey is now 7 years old give or take some months and should be coming off your creidt report. You may need to check and make sure that it is. If you've maintained your credit during the past several years this won't present any challenges.
If you have access to a local credit union, this is where I would suggest starting first. If you'll meet with a good buyer broker in your area they can also suggest excellent lenders whom you might speak with.
To find a grea broker in your area, I've attached a link to ablog I've posted here on Turlia not long ago that you'll wnt to read.