You can change the order that services & classes appear on the Client Scheduler as well as in the Service & Class dropdown when adding appointments. This can only be done by staff with a security status of Account Owner or Administrator. In order to do this, you'll need to go to Settings > Services & Classes and toggle the Reorder switch to On -
You can then reorder your services & classes alphabetically by either the name or the internal name by clicking on the Reorder Alphabetically button -
If you want to reorder your services & classes in a non-alphabetical order, you'll need to hover your mouse over the 
button to the left of the service or class name. When the cross arrows appear, left click on them and drag the service or class to a different spot -
Once you've reordered the services & classes to how you want them to display, toggle the Reorder switch back to Off -
You will now see that the services & classes display in the order you set them on the previous page.