What exactly is the improvement of a Brainwallet in comparison to a standard Bitcoin wallet.
Do not use a brainwallet unless you really know exactly what you are doing. Brainwallets are "expert only", I am an expert of sorts and I do not use brainwallets due to the dangers involved. Many people have had their Bitcoins taken from a brainwallet.
Again, my advice is to forget about brainwallets and stick to the standard wallets out there.
One of the safest wallets on the market is the Trezor hardware wallet, I use it.
Other than that look into
deterministic wallets. They are nice because you only have to backup the seed one time, keep it safe and secret, and then you never have to backup your wallet again. This is cool because making backups of your wallet is just another thing to remember and it is nice to not have to worry about it.
Good luck!