1) Having my own office:
PROS: no disturbances
CONS: (even) more expensive than you might think, especially once you
factor in heating/internet/coffee. Kind of boring with absolutely
nobody to talk to and nothing going on. Can be a bit weird to invite
people over.
2) Working from home: PROS: easy to get to work
CONS: more distractions than you might think, especially if you have a
family with small kids, because people tend to treat you as if you are
"at home" rather than "at work". You really need to have a dedicated
space in your house to even consider this. Some expenses (internet,
electricity, general upkeep) are not be tax deductible since you are
at home. Not super good for mental health since there is no real need
to leave the house for days on end, and all your stressful work stuff
becomes associated with your home.
3) Working in a coworking space: PROS: Nice space, (some) cool people, meeting rooms, a degree of community
CONS: Easy to be "alone in the crowd". You need to make a concerted
effort to make friends, and have people to eat lunch with.