Most of the time when someone mentions 1" stock or 4/4, they really mean 3/4". In a lumber yard wood thickness is measured in quarters. 4/4 is 1", 5/4 is 1 1/4", 2/4 is 1/2" and so on. That is usually sized before it is kiln dried. so if you take a piece of 4/4, kiln dry it and sand two sides you end up with 3/4". If you buy a 2x4 you are really getting something like 1 3/4" x 3 3/4"
When you are planning a project, it's up to you to choose what kind of wood and what thickness. So choose what is available.
You can also laminate two pieces of wood to achieve the thickness you want. Lets say you want 1 1/2" and you only have 3/4", you can glue two board together to achieve the 1 1/2".
The first place to go is a lumber yard or hardwood dealer. If you don't have any dealers near you, try online sources. There are many available. Here's one:
www.ocoochhardwoods.com.