I just returned from my 4th trip to Panama in the last 2 years. Great place for birding. A couple of words of advice, if you don't mind:
Be very careful about following Google Maps driving advice. I've found in Panama, it can take you places you don't want to be. I went to Birding Paradise last year and got stuck on a road that hadn't been traveled in years. I had to walk back to a main road and find a local family with a truck to pull me back up a hill. If possible, get directions from someone local and don't turn onto any roads that you aren't sure about.
I've flown into David twice and stayed in Cerro Punta. La Amistad is beautiful, but was hard to navigate through for an outsider. Be careful about making a wrong turn somewhere and if you think you are on a wrong road, you probably are. For Lagunas de Volcan, you'll probably want to park near the coffee shop at the airport and walk the road to the lakes. There is good birding along the roads.
On my first trip to Pipeline Rd, I was disappointed at the amount of birds I saw there. I went back with a guide this time and it makes a world of difference. They know where to look for specific birds and pretty quickly know if they are in the area or not. There are lots of good guides who are friendly with each other and let others know what they've seen and where they've seen it. I had a target list of about 20 birds and I got good looks at over half of them as well as many others that were not on my list. My guide pointed out two different species of Trogons, a Great Jacamar, Red-capped and Golden-collared manakins, several antbirds/ant pittas and a Choco Screech Owl that I likely would not have seen without him.
If you go to the Metropolitan Natural Park (and you should), you'll do OK without a guide there. I've found the best route is to walk all the way back along the main road from the visitor center and take the Mono-Titi trail. Look for mixed flocks along the hike up. There was one tree (don't know what kind, but had many small berries/fruit) about half way up that was visited by a Toucan, Squirrel Cuckoos, Baltimore and Yellow-backed Orioles as well as several Tanagers and Warblers during the 20-30 min I was there. Great views of Panama City from the top of the trail.
Let me know if you have any questions or need help with finding guides, or places to stay. This is my first post here, so I don't want to look like I'm pushing any accommodations or guides in particular, but I can help if you like.