If you do it yourself, be sure to keep the receipts for the oil and filter for warranty purposes. I prefer to let the dealer do it since, that way, there's an indisputable record that the required work has been performed. Don't let them sell you services you don't need. Insist they only do what is required to keep up the warranty. Around here an oil and filter change, with a "free 19 point inspection" runs around $25.

The most important thing is to make sure they don't overfill the crankcase. The Prius takes 3.9 quarts, no more. Some people put in 3.5 to be sure they don't overfill. I make my dealer put "do not overfill crankcase" on the service order. That way, if they do, I can make them take out the excess.

The manual calls for a 5W-30 oil. I just don't see the value of synthetic oil since, to keep the warranty up, you have to change the oil at 5,000 miles or 6 months anyway. With your cold winter temperatures, synthetic might be worthwhile in the winter.