$360 is about three hours of labour plus oil change materials, which is really on the high side. I very seriously doubt that most shops will take more than an hour total of time working on your bike. First service is a cash grab from people exactly like you, who are not mechanically inclined, but wish to have some piece of mind.
There are honest shops and dishonest shops. The dishonest ones will change your oil, and maybe spend five minutes quickly going over your bike. They certainly won't do anything that takes any time, like valve clearances or chain adjustment. They know that in 95% of cases, a bike is fine after 1000 km.
An honest shop will go through some or most of the check points in your manual. They may shoot some lube here or there, but I suppose the thing you are paying for it if they find anything which is loose or not functioning properly, which might happen that 5% of the time.
Basically, if your shop is dishonest, and I think a lot are, then paying $360 for a first service is a big ripoff. If your shop is honest, they may find something that needs lubing or is out of spec, and you're just paying a big premium for this service. You may never know which it is, as it all happens behind closed doors in the back of the shop.
There's no clear right or wrong answer. But as others have pointed out, you can certainly change the filter and oil yourself (which can be horribly messy; do a search) and check things yourself and save a ton of money. And in doing the work yourself, you will actually have MORE piece of mind because you know what's actually been done. I've had lots of shops screw up things as simple as an oil change on my car.