Saw mills. Hardwood lumber dealers. Lumber yards. Woodworking stores. Private sawyer(they have portable saw mills---the one I use also has a kiln for drying the wood.

The only chemicals intentionally put in wood is when pressure treating framing lumber is done. That wood is not intended for furniture of exposed interior use.

I do not know of any places listed above that will cut to order in small pieces like you want. Some lumber yards micht, but will charge a good price.

The whole point of becoming a woodworker is to get/use which ever group of tools one wishes to use---unpowered hand tools, powered hand tools or powered large tools.

Oh, making the bench or side table you mention is not a nail together job. Screws, maybe, depending on the design. And glue. And clamps while the glue dries. Or old fashioned(but still strong) dovetails and other such joinery----which require some types of tools.

With minimal tools, you should consider corner brackets to attach the legs to the aprons for both table and stool.

Or consider an entry level pocket hole jig

With either, a drill and a screwdriver and Bob's your uncle.

Unless you are using pressure treated wood, I think your fears of toxins are unfounded.

Here is a link that might be useful: See the top diagram of p.2 here

Most all woods are packed with a zoo of toxins that the trees use to defend themselves from insects or fungal infections-- polyphenolics, terpenoids, etc etc, virtually none of which have ever been tested for human toxicity, genotoxicity, teratogenicity, etc. Tropical hardwoods tend to have more, northern hardwoods less. Highly rot-resistant species like redwoods have the most. Chemicals added by humans probably constitute a trivial fraction of the total.

Best advice is to not eat or breathe the wood, especially the finest particles from sanding. Use duct collection and personal protection like HEPA-filtered respirators, avoid fine dust by using hand tools, planes and scrapers rather than sandpaper, avoid tropical hardwoods, especially of you are sensitive to them --many woodworkers develop contact sensitivities to the rosewood related woods.

That said, wood is pretty low on the list of hazards you are likely to encounter in life. I worry a lot more about cutting a finger off than the chemicals I might contact in handling wood.

Look in your Yellow pages under hardwood lumber to find local sources, or contact a local woodworking or turning club. Folks there will probably be able to steer you to the best local sources. Clubs sometimes also have shared tool resources, or check out your local high school or vocational school for woodworking classes to gain inexpensive access to a shop as well as instruction.

I was excited about it until I heard that woods are often treated with all sorts of chemicals that you probably don't want in your home/chemicals that you don't want to come into contact with in your daily life.

Where did you "hear" this?