First and foremost, welcome to the best forum on the internet. Feel free to post some pictures of this new ride. If your screenname is accurate, doggo pictures are also expected
That said, if you call your local Toyota dealer and advise of your wishes, they will usually cover most of what you are asking as part of a routine inspection service.
I always change all fluids when I purchase a new vehicle so I know they're done. So yes, I would do engine oil.
Manual transmissions use gear oil. The biggest key is that it needs to be yellow metal safe. Pennzoil Syncromesh is one of the best to use.
As you know, the car is basically a Toyota. Outside of typical maintenance issues, the biggest flaws of the Vibe are because GM touched it...Luckily those are also generally simple...Radio, AC Clutch/Coil, and Blower Recirculation Gear/Actuator.