Renting a car in Costa Rica

Which part of Costa Rica will you be renting the car in and where will you be taking it? That makes a difference...some places would be fine and others would be a little more difficult for driving. Depending on where you will be going, it will make a difference as to the kind of car you should get as well.

Arriving to Alejuela and driving north towards Arenal with hopes of doing day trips

Renting a car for the Arenal area should be fine...if you go in the rainy season (summer) I would recommend a 4-wheel drive. Some of the roads can be full of potholes and you may want to get off onto dirt tracks to really see some of the more beautiful jungle up that way. If you venture down the Pacific Coast south of Jaco, definitely get a 4-wheel drive. The area just south of there is fine but the further south you go, the more "rustic" the road becomes. To get to the beaches a 4-wheel drive is also useful. If you are going up the coast from Jaco towards Tamarindo it's a bit dryer but the 4WD would still be good to have. Better to have it and not need it than need it or not have it, I say!

Any places to avoid or be extra careful traveling through?

I wouldn't drive in San Jose...super crowded and chaotic and the crime is a concern. Just head out of town from Alajuela and you'll be fine. People do tend to drive quite fast and will pass you against traffic, but just stay to the right and let them. Buses and trucks tend to park in strange places so keep an eye out for that too. It doesn't seem too bad to me but I travel a lot in undeveloped countries so I'm used to far worse. It's not as bad as Mexico or the Phillippines but it is worse than China or some of the Caribbean islands I've been to. I'd compare it to Thailand if that helps?
I have also found that there is, in some places, a lack of directional signage...that can be challenging.
Other than that, the only thing to be careful of is muddy roads after the rain...the mud there turns to a substance that can be compared to ice...it's more like slurry that comes from a potter's wheel. Really slippery and treacherous. I would repeat my recommendation to get a 4-wheel drive vehicle. Other than that, just go with your instincts. We've never had a problem in Costa Rica - very nice people there and a fairly peaceful society.

We rented a car from the Liberia airport and drove all around the Arenal area and Nicoya Peninsula. Absolutely loved it. No problems but we had a 4 wheel drive which I am SO glad we did cause the roads can be pretty dicy, especially crossing flooded roads and stuff we also got a GPS. We for sure would have been lost without it. Nothing is marked every well. We had no problems with crime.