The sooner you file, the better. If your launch is one month away, it’s recommended that you file now on an ITU basis. The priority date runs from the filing date; filing today establishes your claim one month earlier than waiting until the website is live.
Once your website launches, the application can be converted from intent-to-use to use-in-commerce by filing an Amendment to Allege Use along with a specimen, provided the application has not yet been approved for publication. If it has already passed examination, you wait for the Notice of Allowance and then file the Statement of Use instead.
Either way, filing now and converting once the site is live is the correct sequence. The filing fee is the same either way; the only additional cost is the Statement of Use fee payable when use is demonstrated.