Three weeks is a good amount of time to work with. Not sure if others have mentioned the following and I sorry if I end up reiterating. Where you go depends on how you want to do the trip. If you hope to twitch as many species as possible, then yes, follow the Birdquest route and hire a guide/guides. That will cover most spots and species.
If more focused on photography and spending more time with the birds, there are a lot of great sites for that but these stand out:
Rancho Naturalista
Nature Pavilion
Laguna del Lagarto
Paraiso de Quetzales
Bosque del Rio Tigre
Carara area
among various other sites
Keep in mind that it will take longer to travel apparently short distances than expected because of slow, windy mountain roads.
For Osa birds, Bosque del Rio Tigre is excellent and good for logistics. Other good lodges as well further afield, especially Luna Lodge- off the beaten track but top quality forest, very good guide, Turquoise Cotinga is common, etc., etc.
Esquinas Lodge and nearby also get most of same birds including good chance at Uniqform Crake and might be better for logistics.
Johan sums it up for Manuel Antonio, he should know as he is one of the top guides for that area. He and Roy see a lot of good stuff there and nearby.
Carara- one of the best birding sites in Central America. Even if you visit Osa/Golfo Dulce spots, still good to visit for clean up on lowland forest species, mangroves, and dry forest. Note that although Carara is still good, parts of the forest have been getting drier and several humid forest species aren't as common as in the past.
San Gerardo field station- fantastic site even if umbrellabird is not seen. Some overlap with Tapanti (also fantastic).
Some out of the way places to consider:
Laguna del Lagarto- great lowland birding, excellent photography (feeder with toucans, etc.).
Puerto Viejo de Talamanca-Manzanillo- various options for accommodation, great lowland birding in easily accessible habitat often right around hotel, best during migration. Similar to La Selva area and maybe better in some ways.
Cano Negro- actually not too far off the regular track, can be done from Arenal. Several species tough to find elsewhere.
Finally, off the regular birding track because it doesn't fit in with most tours but the habitat is excellent, sites on the road from San Ramon to la Fortuna. This area is a gold mine and little known for birding because tours don't get there. Check it out- I was down that way a few days ago with clients and stopped at the Cocora hummingbird garden as planned. I had heard bellbirds there last month and hoped to get them as well as other cloud forest birds. Weather was bad, hummingbirds were good (White-bellied Mountain-Gem, 7 to 8 other species) but other birds didn't cooperate. BUT, when I asked about bellbirds, the receptionists said, "Yeah, we have still heard them but far away. But, we saw umbrellabird."
I was like, "What? How often do you see it?"
She said, "Oh we see it once in a while. It's common but you know, you never know when you will see it from March to June".
Um, common? Not really, but more regular than other sites!
So, I haven't seen it at that spot but wasn't surprised because habitat and elevation is perfect and I have seen them near there. So, Cocora might be a fair spot for umbrellabird from March to June.
Also, the birding guide at San Luis canopy just down the road said that umbrellabird is pretty much guaranteed at certain times of the year- I still need to find out exactly when.
You can also find plenty of info at more blog (or maybe more than you want to look at!).