I did get to watch it in my phone as I still have internet/cable/phone at home. No matter how big the phone screen is, not the same. I plan to rewatch once the services are reconnected (hopefully on Sunday). I have been a Trek fan since I'm 12 and I've seen every incarnation of Star Trek I can watch. This is certainly another take on Trek and one that clearly does not skimp on budget. I think this is the first time Star Trek has been designed with a high budget for TV. Not even the days of TNG/DS9/VOY/ENT compare.
I thought the story was interesting enough to keep my attention but the first two episodes are more of a prologue to the story. The goal was to establish Michael's character. I wish the Klingons had not been redesigned so much. If they had hair like they did since the movies, the redesign would not be as difficult to swallow. Despite that, the behavior is pretty much the Klingons we have come to expect.
As for timeline, this is in the Prime timeline and they have said it multiple times. I supposed the updated look is to be expected. It is 2017 and not 1966. I don't think non-fans would watch if it had a 60's look to it and their goal is to bring new fans into Star Trek.
I will keep watching. I am annoyed at having to pay for it but right now I'm using the credit I have from the Google Surveys I do to pay for it.