You should probably treat this like you treat money right now. How secure is the wallet in your back pocket?
So my suggestions are to have the following and to move money around depending on your need for access:
offline computer: the computer catches up with the blockchain. The computer's OS (preferably linux) is newly installed and you do not use the internet for anything except bitcoin. After it catches up with the blockchain, you copy the wallet.dat file to a thumb drive and place it in a fireproof safe lock box. Write down or email yourself the address and never turn the computer on unless you want to withdraw funds. This is like your bank account.
create an android wallet. This is like your real wallet. Most people have a limit because they are afraid of being mugged.
create a normal wallet on your computer. This is moderately safe if you take precautions. Others can suggest secure software but I have had no issues with the satoshi client and an encrypted wallet.dat
Create an online wallet and treat it like you would money you pre-pay to any online services.
Put money in these accounts based on the security/ convenience you are willing to risk. This is just an overview and my ideas. I'm sure others can come up with more ideas, etc. Personally, I have an online computer that is dedicated for my Bitcoins. I will likely plan in the future to have more secure storage locations like listed above as my value of BTC grows. I also have an android wallet that I have 0.64USD in right now in bitcoins