As far as baby supplies goes, I packed what I needed for 1 week so that we had some time to find what we needed. Liberia is a big city, and has anything you would need. San Jose is huge and has anything you would find in America.
The photos below were taken in Nicoya and in Ciudad Quesada. Some of the smaller towns like Samara and La Fortuna have less options. We always make sure to buy formula when we are in a big city like Quesada, but diapers and wipes are easy to find in La Fortuna. If I remember correctly, they were harder to find in Samara, but I think I just need to look harder. American brands are more expensive than Central American brands, obviously.
Various shampoos (about $6-$8 per bottle).
Pacifiers ($5 each)
Diapers (about $12-$14 for 48.)
Wipes (these are ~$3/pack)
Formula (~13 for a small can, $24 for a big can. GOLD dust!)
Rice Cereal (I didn't price it in store and can't read it here...)
Just to give you an idea: Shampoos, soaps, detangler, powder, desetin... They have more options for this kind of product in beachy towns. For example, I have not seen detangler inland...
As far as the water situation for T- we buy her all bottled water. She doesn't have her HEP A shot yet so we don't want to risk it. But, we drink the tap water ourselves and haven't had any repercussions. (If you're on the caribbean side, I would only drink bottled water.)
Stroller and car seat in Costa Rica. We are really glad we picked up a cheap car seat on Craigslist before coming. You can sometimes reserve a car seat through your rental car company, but when we researched it out, those cost $15/day. So we paid $15 for a used one in the states with the option to dump it after that first week with the car. The roads are bumpy and windy and for a 9 month old, we felt a lot safer having one. As far as we can tell, it is not illegal to drive with an infant in arms... we see it done allll the time. (also, if there is an extra seat on your plane coming down, maybe they will let you bring the carseat on board so the baby can sleep- luckily that happened for us! Go JetBlue!) So YES, Bring a carseat. As far as a stroller, we did not bring one. Now that we are settled it would be really nice to stroll her... but the stroller would need really big, sturdy wheels to get around. So if you do decide to bring one, then make sure it can handle gravel roads and rocks-- no umbrella strollers here! We have a Kelty Journey backpack that we put T in which works great for us.
If you have any questions about how to prepare for Costa Rica with a baby, just leave me a comment and let me know! Travelling with an infant isn't for the faint of heart, but it is a lot of fun! Memories for a lifetime!