Hammers performs many functions in woodworking. Whether it’s for alignment, material removal, or even for simple nails, hammers are an intrical part of any workshop. That being said there are different types of hammers for different jobs. What makes a hammer good for one thing may make it less optimal for another. For example, when tapping a closely fitting joint into place you may want a soft wooden or rubber mallet. Using the same tool to tap in ten penny nails would most likely end up damaging your hammer. Below I have listed out the three main hammers I use on a regular basis.

Rubber or Wooden Mallet

This type of hammer is great when you do not want to damage the project you are working on but need to have a little extra Force. The soft material will be much less likely to deform the wood of your project. This is the same reason why metal workers will use brass hammers. You can also find interesting variations which include dead blow and screw on hammer faces.
Dead blow hammers have a hollow chamber with lead shot on the inside. This allows the user to transfer more of his energy into the blow. It helps to prevent the hammer from bouncing back. Being able to exchange hammer faces allows you to switch out metal, Teflon, rubber, or wood while only buying one hammer. These two features are more of a nice to have than they are a necessity.
Also it very easy to make a wooden mallet if you’d like a project.
And rubber mallets can usually be found at the local Goodwill for cheap. I’ve included a link to an affiliate version if you don’t want to go through the trouble.

Claw Hammer

The claw hammer is the second must have. This is your general purpose hammer. Good to Pound in and remove nails along with most other striking needs.
This is usually another good tool that can be found at Goodwill because everyone has one. Again I’ve included a link to one of my favorites if you’d rather order online. Double trouble, the price seems to have dropped.

Tack Hammer

CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=303344

The final Hammer I use all the time would either be a tack or ball peen hammer. Both are smaller and meant for finer work. This will help to prevent marring the surface of your project when tapping in finishing nails. For this hammer, you are looking for something small and easily controlled. Some even have magnetic heads to help hold the nails while you hammer. While these may not be as prevalent at Goodwill, you should be able to find them(like all above) at any hardware store. Here is an online Link to a good version.