I would definitely look at the dogs first, but that doesn't mean you shouldn't bet a favorite. There's a system that's been around for a couple years where in the first round you take all the dogs plus the points except you also take the #1 seeds and lay the points. That system has hit at around 58-60% over the last 6-7 years I think (just going off memory, don't have the numbers in front of me). So of course you can go that route, but unless you're betting a lot of money per unit 58% is only gonna get you a very small profit. However, if you look at it from the perspective that the faves (2-8 anyway) are covering at around 40%, while that's not all that good it certainly shows that you can pick your spots with faves and still be profitable.
As previously mentioned, the most important thing is to not feel like you have to bet every game. One of the greatest things about this tourney is the bracket pools everyone gets in, so you already have some vested ineterst in the outcome without any additional coin.
I think it's also been a trend that the faves start performing a lot better from the sweet 16 on.
Hope some of that rambling was useful.