I am trying to buy one full Bitcoin to store as an investment, but with CoinBase's $300-per-week limit, this looks as if it will take a month or more and I'll end up paying way more as the price goes up.
So are there any other safe alternatives for buying Bitcoin? I've looked on eBay but they are charging way over actual value.
Thanks.
Coinbase have strict rules, and they stay with them for specific reasons - it is all about AML.
There is many exchanges where you can buy Bitcoin as safe as with Coinbase. (Bitstamp, Kraken, BTCe)
You can also use LocalBitcoins.
Anyway you must remember that every online service will never give you 100% of security, so always after transaction move your BTC to your offline wallet.