I think the best way to use your funds in order to buy bitcoin, is to go to coinbase and make a purchase there. Their fees are a bit high, but it allows you to directly buy crypto with fiat, and you don't need to first buy tether for example. If you can verify you account on Gdax, that is also owned by coinbase, so by creating an account on coinbase, you already have an account at Gdax, you can avoid fees altogether, both for purchasing crypto, or for trading it.

If you want to just trade, you can stay there, or move some of your funds to bittrex, since it offers a lot of altcoins to trade. If you want to store crypto, then after you bough it, you should at least install a desktop wallet like electrum, and move your coins there. If you really want to keep your coins secure, then a hardware wallet like trezor or ledger is the best option.