(My general approach for BTC is to just buy a few and hold them. If BTC goes global, I'll be happy, if not, and BTC becomes obsolete, no big loss.)
So, let's suppose I chose Electrum, which seems to be one of the easier ones to use.
If I download the wallet to a computer, can I then move the BTCs to an external HDD? Or, do I have to store them only on the computer? It's just that I have a netbook I don't use much with Windows 7 starter and thought I could use that. The question is, what happens if the HDD on the netbook fails, do I lose the BTCs?
Electrum is a great choice. Not only is it easy to use, it is a deterministic wallet.
A seed is initially generated and you can restore your wallet from that. You do not have to worry about your HDD failing.

Is electrum an offline wallet though because i never thought it was, trezor or ledger is the top 2 wallets i would recommend but for what you want i would lean towards the ledger wallet, take a look