I would caution against doing nothing for a while. If you suddenly have an extra mortgage payments worth of funds in your account every month you may find yourself getting used to it and that will make it harder to commit later.
As for rental properties, I kept my last house when we moved and have been renting it out for a few years now. I pay a property manager 10% to take care of everything and finished last year with a cash loss of $3500 and a paper gain of $8500. ie I spent more than I took in, but most of that money went to reducing the principle on the mortgage. I should be cash positive at some point, but the mortgage is being paid down so I look at it as a savings account.
One thing to consider that has been mentioned a bit above is that if you don't have significant assets outside your residence and your future rental property then you will have an investment portfolio that isn't diversified at all. It might be more prudent to borrow against your house to invest in dividend paying funds for the tax break or just direct the value of your mortgage payment to an investment account every month if you dislike paying interest.
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