That said, can anyone explain to me the cheapest method of buying BTC?
Also, what is purpose of buying / saving BTC?
Should I be using an online BTC wallet when buying & storing BTC?
The cheapest method of buying BTC so far is buying via coinbase, it would also be easier for you. Also, it depends on what purpose you have for buying BTC but some like me buys and holds it to grow money. You should be using your online wallet for buying bitcoin, preferably coinbase and blockchain for storing it if it ain't a big amount but if you will store a lot, use electrum or any similar desktop apps to store bitcoin since it is safer than online web wallets.