Updating from 11 to 13

I suggest you Google iOS 13, 13.1, 13.1.1, 13.1.2 so you have an idea of what the changes are before you update. I don't know of any specific issues upgrading from iOS 11.

Also regarding Reminders, when you upgrade to iOS 13 and open Reminders for the first time, please read the warning about upgrading Reminders and how doing so will not allow syncing with Macs that are not running macOS Catalina and iPads not running iPadOS. You will see two options to choose from. Tap Upgrade Later so that you can continue to sync with other Apple devices.

Look through this forum for various issues people who have upgraded have been having with text message, WiFi connections, Auto Dark Mode, update still running for several hours, etc.

Personally, I have had no issues with the current version of iOS 13 (13.1.2) on my iPhone XS.

There is no way to update to intermediate updates. There is no option to select what to update to.

Your device and iTunes will only ever update to the most current iOS version your device supports.

So no, there is no issue updating directly to iOS 13.

See here for details: Update your iPhone, iPad, or iPod touch - Apple Support

Backup your phone first.

If you have Settings / General / Software Update / Automatic Updates turned on then you should automatically get the update. You might have to answer a prompt to continue with the update.

You can also update via iTunes by plugging in your phone and selecting the Update button in iTunes when you see your phone. I always update via iTunes.

If you will launch update your phone will be automatucally updated to most current Version.