Also understand that there is no one “best glue” for every material and repair project. Read all the package labels, as they will list for which materials each is formulated. Don’t overbuy because glue, even in an unopened package, will deteriorate over time.
Make a list of what materials you are planning to glue, whether you can clamp them together until they set, whether they will be exposed to water, etc. When you are able to clamp the parts together, you will generally get a better bond and you can use slower-setting glue.
Glues bond two objects together primarily in one of two ways. The most common way is a simple mechanical bond; the glue flows into the microscopic pores and imperfections in the surfaces of the two pieces and dries. This can form a very strong bond on porous surfaces. Common examples are white and yellow wood glue.
The other way is an adhesion bond; the glue chemically adheres to the two surfaces instead of flowing into the imperfections. This is obviously better for nonporous surfaces than a mechanical-bond glue.
When selecting these types of glues, it is important to get the proper glue for the material you are gluing, or it may not bond well. The most common example is epoxy, and you will notice many epoxies for various materials.
Urethane is one of the newer types of glues available, and it is effective for many materials and applications. It dries (cures) when it comes into contact with moisture from lumber, the air, etc. It basically uses a mechanical bond, and it expands slightly as it cures to fill in any gaps. Gorilla Glue (GorillaTough.com) is available in most places.
Standard construction adhesive is an excellent choice for home improvement projects you are planning. It is ideal if the surfaces are uneven and cannot be clamped tightly together as it dries.
It stays somewhat flexible to handle slight movements, but it is not nearly as strong as most other glues. Nailing or screwing the pieces together, if possible, along with the construction adhesive is best.
If you are planning any outdoor projects, the level of water resistance of the glue is important. Standard white and yellow wood glues are not very water resistant. Construction adhesive, epoxies, and many of the urethane glues are waterproof.
Here is a helpful tip when working with wood that you plan to stain when the project is complete. When using yellow wood glue, do not wipe off excess glue from the joint if some oozes out during clamping. People often try this with a damp rag, and it appears to be clean.
When it dries, the pores, where the glue oozed out, are filled with glue, and the stain will not take. By wiping the excess glue off with the damp rag, the glue gets diluted and flows even deeper into the pores. Often, sanding the area will not even help to get to open pores.
When excess glue oozes out during clamping, do not touch it. Just let it dry and scrape it off later. It will probably have soaked in very little, and light sanding will allow the stain to take.