I use Google Chrome, own a Chromebook and use a lot of their services and I sometimes find things written about how Google steals your stuff and privacy and blah blah blah. I think it's secure enough.
Sounds like you knew the answer to your question before you asked. I use Iceweasel (firefox) not chrome, i use start page not google for my search engine. If you feel google is good enough and respects your privacy use it.