Hello,
I am new to bitcoin, I have managed to set up a wallet on blockchain and on coinbase.
Even though there weren't any major problems (like hack and BTC theft) with those wallet operators (blockchain.info might be a little glitchy sometimes)
To achieve full security it is advised to not store your Bitcoin online, especially not big amount.
That said, can anyone explain to me the cheapest method of buying BTC?
I can tell you which methods are definietly not good. Using PayPal, Debit/Credit cards sometimes Bitcoin ATMs is not advised.
The fees might be too much to handle even in some cases up to 20%. Your best bet is to use standard bitcoin exchange.
Be wary that there is no one universal price of BTC and price might be slightly different, depending on the exchange.
Also, what is purpose of buying / saving BTC?
Look up price charts of BTC. See how bitcoin price is constantly growing?
Bitcoin limited token supply creates situation where your coins will be worth slightly more over time.
Buying and holding BTC to sell/buy something with it in the future is the main reason people own BTC.