The thing is, I think equity is pretty important to have just to get started. It's tough to borrow significant amounts of money from the bank if you don't have equity, and you can always consider paying off your personal mortgage as a bit of an investment. For example, I've calculated with my interest rate on my mortgage that a 5,000 lump sum payment on my mortgage yields about a 5.2% return anually, for at least a few years. It's a low return to be sure, but I think of it as getting a small return as well as setting myself up for something better in a year or two. It's hard to make good money on 200 bucks a month, so may as well slap it on the mortgage and wait for that equity to grow to a point where I can actually use it.
As for good books to read, there's a million and one out there on real estate investing. Some are good, some are not, it's up to you take take out of them what makes sense and go with it.
Rich Dad Poor Dad was the first one I read, and it completely changed the way that my mind worked towards investing. His examples aren't really all that applicable, as you'd need 2 full cups worth of luck to pull a lot of that off, but I found the book fantastic for the philosophy behind what he does. Changed the way I think about things.
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