I'm new into crypto currency and was wondering which wallet I should use in terms of security.
Desktop wallet are far more secure, well that mostly depends on you, but I use blockchains wallet. It's secure, simple and I'm not changing it. What wallet are you using atm?
I am using poloniex and block.io for now. But I was getting paranoid as my coins starts to grow. Additionally, I was having a trouble to log in on poloniex and my password was (or that's what I think) resetted itself or something.
Storing your coins (especially when you have a significant amount of them) on an exchange is a bad idea, as you don't have the private keys. The exchange could have disappeared at any moment like mtgox, and so it is better to store your coins in a personal wallet.