Some of the quest steps require you to win raids, but you can solo 1-2 tier raids. No neckbeard interaction required. Mew's quest line is seven steps, each with 3 tasks. The hardest of which are evolving a magikarp, catching 10 ghosts and catching a ditto. Once you encounter Mew though it has a 0% flee chance so it's a guarantee.
Aside from the special one-time quest, there are now daily field research tasks you get from poke stops. Each task is something like, catch 10 normal mons, or throw 3 great curveballs in a row, and has small rewards like pinap berries, random encounters, extra stardust etc. You can get 1 task stamp per day, and once you get 7 you get a guaranteed encounter with a legendary. Right now that's Moltres.
Right now until the 17th there's a Kanto event going on, gen 1 pokemon spawning everywhere again and double candy / half walking distance for everything. On the 15th for a three hour window is going to be the next community day featuring Flaafy during which time the shiny version will be released with a higher encounter rate. I got 5 shiny Bulbasaurs during the last event.
