The best way to store your Bitcoins is a wallet on your computer or mobile phone as you’ll get a full control over your Bitcoins. A noticeable example of a standalone (desktop) clients is Electrum . Just remember, there are two types of desktop clients, with full validation and simplified one. Full validation requires to download all the “block chain” on your computer, which is very large database (60 GB and growing every 10 minutes) that contains all the transactions ever made using Bitcoin. Full validation in theory provides an extra layer of security and allow merchants to avoid “double spends”. As a normal user, simplified validation works just fine and there is no reason to maintain a complete copy of all ever maid transactions. You are only interested in a small part of the block chain that contains your transactions and it is about 25-30 MB. Online wallets a very popular nowadays as they are easy and quite fast to set-up, don’t require any free space on your HDD and are just convenient, especially when we are talking about relatively small transactions or occasional ones . when you want to transfer you bitcoins from a Bitcoin Exchange to your personal wallet.