You want to reach out to the printer(s) you will be using. What’s common where you are may not be common where I am.
Free may not be an option, unless the printer is local and you schedule an in-person meeting. The samples may be free, but you might pay a shipping and handling fee.
Quite honestly, paper is part of the job considerations. A certain job may require ordering in a specialty paper if that’s what it calls for. A printer may have a swatch deck available to show you options, but they won’t let you take it away from the shop. If you want your own, you may have to contact the paper company and pay for it yourself.