I read the rule book and it appears that the only way to acquire new Adept Powers or improve ones you already have is to increase your Magic Level. Is this correct or am I reading it wrong?

If I am reading this right, since I created my character with Magic 6 and spent 6 points on Adept Powers, if I ever want to get better at Adept Powers now I have to spend LOTS of Karma and Initiate for each additional Magic level.

Yep. Thats why they are Karma sinks (along with mages and Technos). Its one of the things that balance them out. They are more powerful early on, but the Sam can always just spend money. Why do you think there are so many "burnouts" in the fiction. That edge is hard to maintain.

Also, initiation and increasing your Magic are two separate things.

The Street Magic errata has an additional optional rule, though. It suggests that a group could let adepts choose a power point, instead of a metamagic, at initiation.

imo, a power point is not often going to be worth a metamagic technique.

particularly if you are worried about improving your existing powers (as the OP has mentioned) where you could instead pick up infusion (though admittedly, that takes 2 adept powers to pick up fully)

As far as Adepts are concerned, a Power Point is typically far more valuable than a Metamagic.