I live in Cody, Wyoming, have for six years.
There is no waiting period on guns, only the regular call to Washington DC. If you purchase from a private seller, no check or record is required at all.
You can buy any type of firearm other than handguns at 18. I purchased my SKS at 18.
You do not need any form of permission to open carry a firearm. There is no age limit. If you legally own the gun, you can carry it. And remember, you can legally own a handgun at 18. You just can't buy one from a federally licensed dealer. Anyone who is trying to sell a handgun privately can sell to anyone 18 and older. The ONLY limit here, is that you cannot sell to someone you know is a felon.
I open carry everywhere, starting at 21 years to the day. (I had a gun picked out at a licensed dealer). I now own two handguns, and one of them was purchased privately. A few days ago, I let my friend borrow my second gun, (he is 19) and we open-carried all over Cody.
If you have anymore questions, you can send me a message and I will try to answer. Let me know where in WY you are moving. And remember, you are not doing anything wrong by OCing legally. Always be respectful, always be safe, and always be informed. Don't let anyone make you feel like you are doing something wrong if it isn't illegal. Your choices are yours. No one has the right to take them from you, or to make you justify your choices.
Good luck, and welcome to the site. I got my confidence to OC and the answers I needed from this site. Everyone is great!
Hope to see you around someday.