What site to generate cold wallet?

Hi Bitcointalk,

I am new and just recently bought a bitcoin. Right now I have it in blockchain.info wallet but im so sure if I can trust that site. I plan to go cold storage but not so sure where to begin. As a nervous newbie I have some questions:

1. I read somewhere on the internet that bitaddress.org is where I need to get my private key and wallet but I'm not sure if what I read was trustworthy source so I decided to ask this community. If bitaddress.org is not legit then can someone please direct me to a legit site to get my cold storage key?

2. Is it correct that for cold storage there's no public key but only a private key and a wallet address?

3. Is brain wallet (in bitaddress.org) pretty much like block chain.info where there's a 12 word passphrase I can use in case I forget my private key?

Sorry if this is too much info to ask for or if I sound like a dummy but I'd love to hear from you. Thanks in advance.