This is actually quite a complicated question. For one, things can change rapidly. For example, the interest rate penalties for high loan to value (LTV) ratios used to be higher. I believe they have been reduced in many cases as part of the effort to improve the housing market. On the other hand, a lot of loan regulations have gotten stricter to avoid bad loans entering the market again. Basically, rate changes related to your LTV need to be discussed with your lender.
Private Mortgage Insurance (PMI) still needs to be purchased when your LTV is greater than 80%. PMI is typically equivalent to a 0.50% to 0.75% interest rate hike for the period it needs to be paid. Some lenders advertise PMI-free loans even when your LTV is greater than 80%. The PMI still has to be purchased, but for these loans the lender buys it. They will pass this cost on to you via a higher interest rate - there is no such thing as a free lunch. Because your interest rate won't change for the life of a standard 30-year fixed rate mortgage, this interest rate, even if it results in lower monthly costs than buying PMI, could very well cost you more in the long run. Again, go over the details with your lender.
When it comes to deciding between making a larger down payment and buying PMI (or accepting a higher interest rate to cover PMI expenses), you have to look at the best use of your money. My previous post on whether or not to prepay your mortgage could be helpful in evaluating your options. Personally, I would rather avoid PMI than invest a few thousand dollars, say. Whatever you invest that money in would have to earn you more than the PMI payments and extra principal and interest payment amount (minus taxes on the interest and PMI, since PMI is tax deductible like mortgage interest). In fact, this should be considered an addendum to my previous post: The return needed to overcome PMI probably warrants paying extra principal at least until you reach 80% LTV. Psychologically, I just hate the idea of paying private mortgage insurance because it only benefits the lender.
Paying extra principal at the beginning such that you have less than 80% LTV ratio mostly follows my previous post's recommendations. The only difference is that the extra principal in this case does reduce your minimum monthly payment. When determining the terms of your loan, though, you have another option to reduce your payment: you can pay points to reduce your interest rate. As you can see using my refinancing calculator, reducing your interest rate can reduce the interest portion of your payment more than the total monthly payment amount in some cases. You have a choice in which number you use in determining your break even point, but obviously the total monthly payment might be all you care about.
I would make a point-paying calculator, but the cost of each interest rate reduction isn't always the same. For example, it may cost you half a point to move from 5.000% to 4.750%, but another half a point to move from 4.750% to just 4.625%. The user interface of such a calculator would be clunky at best. You can use the refinancing calculator fairly easily to get individual values and compile your own table of break-even times, though. Just find a payment amount for a 0-point loan and plug that into the current loan information fields. Then zero out the closing costs and adjust the points value and find the resulting interest rate entry.
Overall, I would tend toward a 20% down payment if you can afford it so you can avoid PMI. After that 20%, paying points will usually reduce your monthly payments more than extra principal. I paid half a point on my first loan, I think, and zero points on my refinance, other than the quarter-point fee I paid to waive escrow. For the most part, it comes down to what you feel comfortable paying up front versus owing later. I'm not sure there's ever a clearly wrong decision!
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