Alex,
Have you considered partnering with other investors? If you can legitimately cover a downpayment of a minimum of $15,000 then I would suggest you cut that to $5,000, form an LLC with other investors (maybe 9 or 10 others) who can also bring $5,000 individually and go shopping for deals. I think that cuts down your need to find more money, provides the downpayment you need for multi-family properties in your area, and increases the number of properties your group can eventually have under their belt. You just have to decide if you want to hire a property management company (I suggest you do that) or if you or another member will handle it on your own.
And I agree with what Tom Meade said previously, in the sense that you should only look for properties that cash flow immediately or with an associated rehab can cash flow nicely. When I speak about carrying costs I am asking you to consider costs for vacancy, repairs, insurance, mortgage, taxes, etc. Basically, what amount of reserves do you need to cover these expenses if your tenant(s) isn't doing it for a few months.