Is the Internet safe for e-commerce

Generally speaking, I'd say - Yes.

I think in many cases, there's actually increased privacy of your financial transactions. The automated process mean fewer actual people are handing your credit card information.

Like tradition brick and mortar shops though, not everyone that sets up a website is trustworthy of doing business with. I certainly wouldn't give my credit card information to just any on-line seller...

Most ecommerce sites are trust worthy nowadays. If you have concern about a website don't use it.

Big brand name stores are the safest to stick with. If I am concerned about buying something, I will use electronic check through my bank account or paypal. My bank guarantees theft protection and if something does happen they will cover all expenses. That is another option for you.