Hello @Trent Reeve
The other posts explain very well how to start out with a STR and I would like to add to what @Alex Pino mentioned. While an LLC is not required for a single property (or multiple for that matter) it is beneficial to further reduce liability. This may depend of course on location and other details so that is up to your disclosure or with further information and discussion with a CPA.
If you do set up an LLC, you can set it up in a separate state but may be required to file taxes to that state respectively. You may also be required to have a registered agent for the LLC if it is a different state so do bare that in mind and do look into it before proceeding.
You would not need a tax ID for the property if you are not getting an LLC as you as the individual would be the owner of it.
Regardless of whether you go with an LLC or not, I highly agree with having a separate bank account for the property specifically to keep your transactions organized. Having a mixed account can lead to a lot of confusions in finance managing. A separate bank account also helps with when it comes to filing the taxes.