What saw blade to use will depend on what you are cutting (picture frames, floorboards, railway sleepers etc) and the type of cut (finish) you want.
If cutting floorboards, etc, a fine tooth blade will give you a better finished cut. If a fine finish is not required, then use a larger tooth blade.
Most standard blades come in either 24 (rough), 48 (medium) or 60 (fine) teeth.
Maybe consider a 'thin kerf' (80-100 tooth) blade if cutting finer timber and laminated boards. - darylhewston
A consideration for the correct saw blade is whether you are Cross Cutting (sawing across the grain) or Rip Cutting (sawing along the grain). Generally Rip Cutting blades have fewer teeth (16 to 40) whereas Cross Cutting blades have more teeth (40 to 80).
Most Hobbyists and DIYers would probably settle for a combination blade which is suitable for both. Combination blades are structured differently, usually having groups of teeth consisting of 1 rip cut tooth and 4 cross cut teeth with deeper gullets, Combination blades come in 40, 60 and 80 teeth.
Cabinet makers and professionals will generally use a dedicated blade type for Rip or Cross and also for varying timber or sheet types. How much you invest will be justified by how much use it will get, high quality saw blades are not cheap. - Wayne
If you are cutting thick timber (i.e. sleepers) do a few passes and go slowly (but not so slow that you burn the timber). If I'm cutting a 40mm slab, I will set up a fence, then do the first pass with the blade set to 20mm, then put the blade down to 40mm to cut through the rest. - She_Skills