Hola Rocco & Valerie
We did exactly this in January of this year and then moved here in August.
We rented a car from Hertz, using our Hertz Gold club membership. You can sign up for a gold club membership online. The reason for using the gold club membership is that it gets you some extra perks. Also, Hertz was the only rental company that we found in Panama that gives you an emergency phone number to use, so that if anything happens to your car, you call them and they come get you.
We bought a Garmin GPS unit and a Panama map system for it. We got the largest screen possible so that it would be easy to use. I will look up the info on where we got the map system as it is not available from Garmin. However an alternative is to hire a taxi and follow it out of Panama City, trying to get away from the airport and on the Pan-American Highway with out either of these will have you going in circles and getting lost. Traffic in Panama City is worse than New York and with all the construction going on streets are blocked and there are lots of detours.
You will also want to get a letter from the credit card that you will use to rent the car detailing their providing the extra insurance for your rental. Otherwise your cost to rent a car in Panama can double or even triple from what your reservation will say with all the extra insurance. Even at that you may have to give them a LARGE deposit on a credit card (DO NOT use a debit card, use a credit card). We got our letter from USAA, our insurance and bank credit and debit card provider. They provided the letter in both English and Spanish. Be prepared to argue with the person at the rental desk about the rental cost and the insurances required. Most likely you will have to ask to speak to the supervisor. You will have to take the personal liability insurance, do not go without this, because if you get in an accident and there is someone injured and you do not have this insurance, you will immediately be taken to jail!
When you go outside to pick up your car, go over it with a fine tooth comb. Use your camera or Smartphone to photograph every ding, dent, scratch, etc and make sure they are all noted on the pick up inspection report. When you return the car, make sure you go over the car and get a sign off on the return that there are no "new" ding, dent, scratch, etc. Show them your photos and the inspection will go much faster. Under NO circumstances leave the car without getting the turn in inspection report signed off. If you do, you may find that your credit card will be charged for a big number of dollars for some dent or scratch. They will charge you not only for the repair, but also for every day the vehicle is out of service.
Do not get a really small car, a compact is best and do not take it off the main paved roads. If you take it off the main roads and it get stuck or in an accident, it is expensive to resolve.
Follow the speed limits. Use WAZE, if you are not familiar with WAZE, download it now to your Smartphone and get use to it. It will save you from getting tickets as it will tell you when the next policeman is coming up, so that you can be sure to at or slightly under the speed limit. By the way, check with your cell phone provider as to what your charges will be if you use your phone in Panama. My wife used hers to read emails and Facebook and it cost over $200 for only 2 days use. She called the provider, AT&T, and they gave her a credit because she thought that she had turned off the data usage and was using WIFI, but was not.
Once you get out of Panama City the driving is easy and the bigger gas station do accept credit cards for gas. Gas here is by the liter so it may seem cheap, but is regulated by the government, so most stations are within a few cents of each other.
Do not want to make it seem like you should not rent a car, but it is very different than in the USA. If you are spending anytime in Panama City, do not try to drive in Panama City. take taxis or hire a driver. We have been using Luis Arce as our driver and tour guide for quite some time. He is Excellent and has a van. When we first arrived in Panama we had 4 large suitcases, 2 carry on bags, 1 very large backpack, 1 normal backpack. After a week in Panama, we then had Luis take us to the Decameron to pickup the car we bought and we had all that we arrived with plus 4 additional large boxes and everything fit in his van. Luis lived in New York for many year, speaks good English and knows all of Panama. He also has access to many other vehicles and arranged for a box van when we need to pick up our 4'x4'x6' crate at Delvi and have it taken to Pedasi. We highly recommend Luis. Luis is very busy, be assured he will email or call you back as soon as he can, please give him at least 24 hours to do so.
Luis Arce
+507 6536-1179
luistaxi777 @ yahoo.com