Are you buying or renting? Your question is under home buying but generally an apartment is rented, and your screen name says acquisitions, which would tend to indicate you are buying. The initial earnest money deposit when purchasing a property can be any amount the seller will agree to, it could even be $1, but I certainly don't recommend you try to do that, it would tend to indicate you don't have the money to complete the purchase (and to be honest it looks as though you don't have the money anyway). However, you could try $100 but $1000 is more the norm. There is usually a second deposit also required at some point before the closing.
If you are looking for a mortgage you could try a USDA loan, those are 100% financing, I don't know if Atlantic City qualifies as a 'rural' area but I have been amazed at the areas that DO qualify so it might be worth a try.