Q:

Does a long time storage wallet need to be online?

I have a offline computer that has never been connected to a network. I use this computer for long time storage of sensitive data, all data transfer to and from this computer is done by USB memory. I want to move most of my bitcoins to this computer, so will it work this way:

Install bitcoin wallet on the offline computer and generate public address.
Send bitcoin from my online wallet to the address of the offline wallet.
Download bitcoin blockchain on a online computer and move it to the offline computer by USB memory?

A:

You don't need the 3rd step for long-term storage. You don't plan to spend your bitcoins any time soon when you're looking for long-term storage. If you download the blockchain now, it will long be outdated when you want to spend your money and you may as well only download it then. Or you choose a wallet which doesn't require you to download the entire blockchain.
Technically, the computer holding your private key doesn't have to be connected to the internet as a transaction can by signed by software running on that computer, then be transferred via a thumb drive to computer connected to the internet, and be broadcast from this second computer. This has the disadvantage that the blockchain has to be downloaded to the point where the transaction which was made to the long-term storage address has been confirmed. So you'll have to decide between [downloading the blockchain and being able to spend your money without the computer holding the private key being connected to the internet] and [not downloading the blockchain but having to transfer the private key to an online computer when finally spending the money].
Electrum can do this. I don't know whether other wallets can do it, too, because I only use Electrum.
Note that you don't even have to have any computer hold the private key. A private key is just a 256 bit number (default case; few restrictions on the range of values it can take, but almost all 256 bit numbers are valid private keys and that's really all there is to them, no magic involved). Numbers can be written down on paper.
Alternatively, you can use a brainwallet.
All 3 have things you can lose to lose your money:

Wallet on computer:

Malware can delete the wallet or encrypt it. (Can happen through infection via thumb drive.)
Your hard drive (+ backups) can break.
Some larger damage (e.g. house burning down) can break the entire computer, including the hard drive.

Paper wallet:

You can lose the piece of paper.
Damage can happen to your piece of paper. (The writing can fade, a fluid can be poured onto it, etc.)
A member of your family might find it and throw it away.
If you print it, a part of the private key may not be printed. This actually happened to someone who asked for help on this StackExchange site. They printed their private key in wallet import format but it didn't entirely fit on the page.
If you write it down by hand, you might make mistakes.

Brain wallet:

You can forget the passphrase.

Combination is possible:

If you have a private key on a computer, you can write it down. Again, the private key is just a number.
If you have a private key written down, you can make it a wallet on a computer.
If you have a brainwallet, you can write the private key down or make it a wallet on a computer.¹

¹ You can't go in the opposite direction without actually remembering the private key (which is absolutely not recommended). Remembering an Electrum seed (which looks like this: "constant forest adore false green weave stop guy fur freeze giggle clock") reliably may actually be possible but I still advise you to use the standard method of creating a brainwallet if you want to use one.

