There are a number of factors that will influence the saw blade you choose. These range from the type of material you need to cut, to the type of cuts you need to make and the finish of the cut that you require.
The usual saw blade that is sought is one that will provide the best and smoothest cuts that you can get. So it follows that an understanding of TPI or teeth-per-inch is necessary, as this measure helps to understand the cut and finish you will get. TPI is a good measure to help you select the best saw blade for your use.
When it comes to TPI and saw blades, there is often a generalised rule of the higher the TPI, the smoother the cut, however there are factors that affect the overall quality of the finish you get.
First up, the teeth per inch on a saw blade affects the speed in which you can cut. Lower TPI means less teeth, more gaps. This means that the saw blade can cut quicker, but as the spaces between teeth are deeper, the cutting action is quite aggressive. So you will tradeoff speed for a finer finish with higher TPI saw blades.
In terms of your finish though, you need to be aware of the higher level of friction of higher TPI saw blades and possibility of burning your wood as the blade goes through your material. Also there is an increased chance of binding when using high TPI saw blades due to the much smaller gaps between teeth and the build up of saw dust.
In general for a band saw, the saw blades required will be based on the type of cuts you make. So for tight curves, a 1/4 inch blade with high TPI, then a range of blades with about 3 TPI such as a blade of 1/2 inch for general cutting and a 3/4 or 1 inch saw blade for resawing.