Try to use localbitcoin and paxful, both exchange platform is easy to use and safe and secure. You don't need to use any verification for creat an account there.Did not mentioned what currency you want to use for buy bitcoin? will you tell us about the payment processor.Both two platform that i said in upfroont there you can found a lot of payment processor also for paying.
I do purchase and sell the bitcoin in localbitcoins.com always. Now i am really worry about the fees to deposit the bitcoin in the exchange wallet. Previously there is no fees to deposit bitcoon only the have fees for sendimg btc from there. It should recover soon to have huge number of users.