There are taxis at the airport you can take. That’s what I’d do. There are booths inside the airport where you tell them where you are going and they will tell you the fare. Probably $25 to $35 depending where in Quito you are going. You pay, they give you a piece of paper that you take outside and give to the guy who puts you in the first taxi in line.
Otherwise, if you really want someone there waiting for you, you can ask your hotel to arrange this for you. There is an expat with a transfer service. His name is Jack Abercrombie and his email address is journeymanjack.com@gmail.com. These last two options will cost more.