I'm not sure about this,but I don't believe you can take a rental car across the border.
NB

if you're not used to driving in countries other than the US and Canada AND Cancun bus drivers scare you, then you might want to consider visiting some of the smaller and much less populated cities in the countries you mentioned. Stay away from big cities and touristy areas and the driving styles of south/central america may be less frightening for you.

i dont think you can rent a car in the borde

I can't really say which country is safest, but you might feel most at home in Belize. It's super, super laid back and English is the official language. I've never met happier people in my life. I spent 8 months in Central America, including these three countries. I'd advise against driving in Guatemala. The roads are often in very poor condition, and I think that's the rainy season and the unpaved roads will be a nightmare. Driving in Guatemala City was terrible. I got stuck in rush hour traffic there for hours!

Here are some spots I recommend:

Panama:
Bocas del Toro: get some scuba diving in, take the boat through the mangroves to these beautiful islands, lay on the beach
Boquete: the people are so friendly here! There is lovely hiking in cool, misty mountains, waterfalls, lots of flowers and coffee plantations. You can also hike nearby Volcan Baru from here.
Panama City: I dug the capital. The canal is nothing too special, but the city is a fascinating mix of modern and old, with Spanish ruins, the old city of Casco Antiguo which looks like the streets of Havana, and the new city, with neat cafes, restaurants and night clubs.

Belize:
San Ignacio: Cool little town that is a great base of operations for exploring the jungle, caves and mayan ruins. Aktun Tunich Muknal cave is expensive to go to but uterly worth it, just a stunning cave system with old maya pottery and remains of human sacrifices. You can also visit the ruins of Xunantunich (you can take thne bus here) or take a tour to Caracol
Caye Caulker: dive the Blue Hole, sit around enjoying the tropical atmosphere, eat lobster and dance on the beach at night

Guatemala:
Antigua: feels very European, with its old Spanish architecture, cathedrals, cobbled streets, except for the volcanos. You can hike the nearby volcanos, study Spanish (there are a lot of young backpackers here doing that), party at rooftop bars, finally get a good espresso and cheese cake, or get lost exploring. It's a charming city, although it doesn't feel like Guatemala
Lake Atitlan: beautiful and peaceful lake in the highlands. There is hiking, lake diving, and plenty of partying depending on what city you go to. I prefer Santa Cruz, which is very small and quiet and enables you to interact with local people.

You have to pay extra here in Belize to drive rental cars across the border...so coupled with the fact that the drivers here suck ass, you really don't want to waste money on a rental car. I tell all my friends who come to visit me to fly into Cancun, party there a night or in Playa, take the bus to Belize, party here for a while, and then do Tikal, and Rio Dulce in Guat, and then whatever they want to do after that, be it taking the Livingston, Punta Gorda loop or the Palenque loop back to Cancun. If you want to rent a car, save that until you are in San Ignacio since we have the most sights to see in Belize. Have fun!
-MM

Cath, amanada does hit the nice places well...you can move around by public transit fairly easly and not worry about it at all for safety,just rememebr that in gutamala yes roads are bad and there are frequent roadblocks,ie busses searched and everyone off passports scrutinized,etc etc. Belize you may like orangewalk as well,of the three you can foloow the routa maya tour going west from cancun to chichen itza,then to to compeche,back through the routa puuc smaller maya sites.... leading to Tikal,and from there go into belize out to the cayes...I like key cauker for the diving and the laid back atmosphere...feel free to contact me if you want more info...don't drive yourself ,there are many places to get to all served by busses and crossing borders though allowed is subject to many scams,,,,buy our insurance etc etc

Cathleen,
Travel in Central America is becoming more and more tourist friendly. If you are considering going all the way to Panama I would suggest you conside Costa Rica. A friend of mine was there about a month ago and he told me he had a great time. Belize would is another option since the folks there speak english. If you want to see some really cool Maya sites then I suggest going to Guatemala. Guatemala is a really beautiful country, my family is from there, but sometimes roads arent the best. I guess it depends on what you want. You want to chill on the beach then go to Costa Rica or Belize. If you want some culture and what not then go to Guatemala. The Yucatan is also a great option.

good day,

Armando