What should I pack for a trip to Costa Rica?

You'll be fine in tank tops, no worries about bare shoulders in Costa Rica. Since you're backpacking pack a rain poncho that can cover you and your backpack when it sudden downpours. For shoes, yes bring some sneakers, old sneakers, sandals are good too, if you are going to beach areas a pair of watershoes are handy and they also come in handy in other wet areas. Bring good insect repellent, REI sells a good brand called "Jungle Juice", its 100% deet, you can order it from them online. Bring various sizes of zip lock baggies to keep things dry and to keep food. Yes a hat is good, not so much for ticks but to block the sun. Bring good sunscreen. Pack clothes that dry fast, you may want to pack those small Tide laundry detergent travel packs, a short clothes line and a few clothes pins to do laundry on the fly. Have a great trip, it sounds awesome.