Thanks for the quick reply. I was finally able to fix the problem. As noted by several others in various forums, PayPal WTS apparently triggers a second email notification if Conditional Actions aren't set to "Check the order status" with the argument set to "In Checkout". This seems to be the answer I was looking for, using only PayPal WTS. There are also additional settings that may need to be applied to distinguish PayPal from other payment methods if others are enabled.
To clarify the exact steps I took for Ubercart/PayPal beginners like myself:

1. In Paypal, I set up the account to be a business account, and in Profile > More Options > My Sellings Tools > Website Preferences, I took the following steps. Turn on Auto Return with the following Return URL (https://www.example.com/cart/checkout/complete (substituting your site name in place of example.com, and change to http:// if not using SSL). Use this and not http://www.example.com/uc_paypal/wps/complete, which was intended for an older version of Paypal/ Ubercart. All the other settings should be off, with the exception of "Paypal Account Optional,", I left IPN off, and it seems OK.

2. I uploaded md-2's UberInvoice Module(thanks again), followed the instructions and edited the templates to my liking.

2. In Drupal/Ubercart > Store Administration > Conditional Actions > Triggers I edited the E-mail Admin and E-mail Customer notifications to enable new templates in the Actions Tab. This is also where I had to add a Condition Group to the email notification in the Conditions Tab to "Check the Order Status" with the argument set to "In Checkout".

Hope this helps someone else with a similar problem.
It took a while for my notification email to show up after changing the settings for the first time also, for some reason, which added to my confusion. Now it seems to work well though.