In Western Blot when you decide to choose the primary antibody make sure that the primary is specific to the protein of interest and should be of a different host species than the sample. Also, the primary antibody should be validated for use in western blotting, the information for which will be made available in the package insert for the antibody which you will purchase.
Another point to remember is that the primary should be specific for either the denatured or native conformation of the protein of interest, which will depend on the type of PAGE (either SDS or native) you perform.
Further, choose a secondary antibody directed against the species of the primary antibody. So, you will need a secondary antibody that is raised in a species different than the host species of the primary antibody. For instance, if your primary antibody is raised in a mouse, you will need an anti-mouse secondary antibody raised in goat, rabbit, etc.
If you would want to perform multiplex Western Blot, use primary antibodies from different host species for each target being probed. Ideally, use a combination of antibodies from two distantly related species such as rat and rabbit, avoiding the combinations like mouse and rat or goat and sheep. This will help in the selection of appropriate secondary antibodies to minimize antibody cross reactivity that could affect your end results.
to follow the very complete answer of Malcolm Nobre .
I would add as a final step to always check the litterature associated with the antibody you're gonna buy to see if it actually works, at what dilution, in what cell type, etc.
Quick but key bit of information for your secondary antibody. Western blots require that secondary antibodies are conjugated to something. In brief, there is an enzyme stuck to the antibody, it is the activity of that enzyme that you are detecting. Make sure the conjugated antibody you choose works with the detection systems you have available.