I am using blockchain.info from long time without any problem.
yes blockchain.info is fully trusted and highly trusted forever
why?
read this for example!
https://www.cryptocoinsnews.com/gentleman-hacker-returns-stolen-bitcoins-blockchain-info/the idea of bitcoin is that you have no other (third parties) who keep your money safe for you.
a online wallet is maybe good as a temporary solution. but i would never trust in long term!
Do it oldschool and download bitcoin core, the orginal bitcoin client. if you like bitcoin then you have the required space on your harddisk ...