if you pc is clean being connected or not will not make any difference,[1] if you knwo that your pc is infected(usually something wrong happen in this case, like cpu usage too high, strange filename ecc...) then it is better to move your wallet in another storage(offline is better)
my point is that you can have a online safe computer, in my case i have a wallet that it is always online with some btc, no one has stole those bitcoin from my desktop ever, they are still here[2]
[1]Yes it makes a difference. If your PC is disconnected a hacker can't gain access to it. While it is connected, he can. There are infections that can't be detected by anything, not by the average person nor software because of its complexity. However, a security researcher (or a group) might.
I'm going to assume that you haven't heard about The Mask (a.k.a. Careto); you should look into it. Luckily AV's can detect it now, however there are probably a lot of these out there (e.g. finfisher).
[2] If nobody has stolen your coins, that doesn't mean that they won't. Depending on your balance you might not be a likely target. We've seen a lot of people (over time) ask for help on the forums because their wallets were compromised.
My suggestion is a few USB's or paper wallets. Either one works great as cold storage. Just make sure they are stored in safe places.
-snip-
I wouldn't use USB's. They are have quite huge vulnerabilities and are prone to failure.
I'd recommend paper wallets as well. If you really wanted to store your Bitcoins for a longer period of time I would suggest the following:
1) Buy a type of stone (e.g. marble)
2) Get your private key and engrave it into the stone(It would be risky to let someone else engrave it; if he's familiar with Bitcoin he could steal your funds)
3) Place the stone somewhere and cover it (I have a few ideas) or bury it
4) Download D-BAN:
http://www.dban.org/5) Overwrite your HDD 35 times
6) Put HDD in a Microwave
7) If you have the proper tools, melt the HDD
The last 3 steps might be exaggerating (7 overwrites should be fine) but this is how I would stash my (potential) billions. Just make sure whatever you do, you make backups.