Getting to Puerto Viejo (Limon province) from San Jose or Limon is fairly easy -- there are 5 direct busses per day station to station public buses for less than $11.  The buses are quite comfortable and are safe but are not air-conditioned.  Do not be turned off by the idea of public bus to Puerto Viejo.  They are quite safe and absolutely the best value.  They also will almost always be faster then any tourist mini-shuttle as they are direct with one 2 stops (Cahuita & Limon)

If going by bus, it is best to travel light.  If you can keep it down to one small bag or pack, you will have a much easier time getting around.  But there is no problem with also putting larger luggage under the bus.

If you take the public bus, it is best to get your ticket in advance if you can but the bus companies only sell tickets in person. There are several companies who will pre-purchase your ticket for you for a fee if you're heading straight to the bus from your arriving flight and some include airport pickup. Companies include A Safe Passage and Gecko Trail Adventures

There are also scheduled A/C tourist minibuses which pick up and drop at most hotels. A private driver and vehicle can easily be hired through a reputable travel agency for a fixed point to point price or a daily rate. And all the major car rental agencies operate in San Jose as well although getting out of the central valley can sometimes be confusing but once you're on the highway it's easy enough. 

Bus and tourist shuttle schedules can be found online from several sources including Puerto Viejo Satellite .

If you're coming from Arenal, there is also a tourist bus but taking the public bus is complex and requires a change of buses and bus stations in San Jose. To come directly to the Caribbean from other Costa Rica destinations, you'll either need to hire a private vehicle or drive yourself or spend a very long day making connections in San Jose.

One the most popular ways to getting to and from Puerto Viejo, San Jose & Arenal is taking the rafting excursion.  They will pick you up at your hotel in any of these 3 locations, feed you breakfast, take you rafting, feed you lunch on the river and then take you to your hotel in any of these 3 locations.  $99/pp.  Ask your hotel to arrange this or book with Exploradores directly.  

If you plan to book private transportation online, read your reviews of the tourist group first and don't get sucked in by picking the cheapest.  There are many websites that will take your credit card information and fail to show up when it is time to deliver.

If you plan to rent a car, a four wheel drive is nice, but not an absolute.  The roads are fully paved right to Puerto Viejo and beyond.  Very few potholes these days.  If conditions are generally good, you can count on 4 to 4.5 hours.  Note that traffic, weather, road repairs etc can add to this.