You can travel just about anywhere in Costa Rica on a budget. Of course some places are cheaper than others but every major tourist town has hostels and sodas where you can eat cheap local food. The public bus goes just about anywhere but you’ll find that it is more difficult to get to some places. Tenorio/Rio Celeste is one example. Because it’s so remote, it will take some time and many bus transfers to get there from Playa Grande. Getting from Tenorio to La Fortuna is doable and there’s a bus from La Fortuna to Monteverde. You can also get from Monteverde to Uvita via Puntarenas, we believe, but it will be a very long day of travel. You might think about breaking up the trip with an overnight somewhere along the way. The obvious outlier in your itinerary is Puerto Jimenez because it’s so remote. It will take a long time to get back to Liberia afterwards so you may want to think about ending your trip in Uvita instead. Five destinations is much more doable in two weeks anyway, especially since you’re planning to take the bus, which makes it take longer to get between places. This is a good website to help you plan your bus travel: http://www.thebusschedule.com/cr/index.php
Another thing to think about is that some of these places are touristy and will be busy in January. Playa Grande is close to Tamarindo, which is very touristy, and La Fortuna and Monteverde get busy as well. You might want to at least swap out Monteverde for San Gerardo de Dota/Los Quetzales National Park for your cloud forest experience. You might also like San Isidro, an authentic little city south of San Gerardo on the way to Uvita. We have a blog post about it here.