I went to Costa Rica from México, so it was rather cheap to get there. I would suggest getting a ticket to the US, and then US -> Costa Rica.
Costa Rica is amazing, be sure to make the trip to Tortuguero and also Arenal is stunning (which recently erupted).
If renting a car, full insurance with no excess is a must - the roads are not always well maintained. Also, whilst I managed in a Yaris - the 4WD option is recommended!
Tim