Personally I would go with the emergency fund for the most part. Once I had a couple of months expenses in savings, I would divide what I was putting in between the emergency fund and a Roth IRA. When I had 6 months of expenses saved, I would still be putting money in Roth and the e.f. but but a bit of it in a car replacement fund as well -- every month. Once I had about 12 months expenses saved and my Roth and other retirement vehicles exhausted, I would just invest in some other way, I wouldn't keep it all in a savings account. I personally think the options of disability and life insurance would be more of a priority than the mortgage.
I have been trying to make the same choice. No consumer debt, no car loan, have 4 months expenses saved plus I put $ in a car fund every month. Next goal is disability insurance (already have life). I don't have a mortgage but I am ready to buy this year. Once I own the house, I will put some $ in a house repair fund, increase my emergency fund, and still hopefully keep maxing out my Roth. I do tend to max out the Roth as a priority over increasing savings because you can't get the opportunity again to put in that $6000 (yes, I am over 50!) BUT in case of a real emergency, I could take out the principle without penalty. And the funds I am invested in seem relatively secure as they showed a decent return even in 2008 with the stock crash and all. The IRA is also diversified into higher and lower risk options.
Eventually I am considering switching my Roth to a self directed IRA and buying investment rental property; but at this time the amount just isn't there.
Truth is, once you pay off consumer debt and are used to simply living below your means (and have learned how to really enjoy it), pretty much all of the options are good. Paying down my mortgage, once I have one, would probably come after maxing out retirement fund (I only have option of Roth at this time), but BEFORE investing in some kind of side business. Advantage of having a side business is not only making money, but it also increases your investment options, as then you can open a Solo 401K and you can also self direct THAT so you could, for example, buy a small business tax liens or rental properties within your Solo 401K.