To get altcoins do I need to buy them with the part of a bitcoin
No you do not. You can actually mine them yourself using your CPU or GPU, depending on the coin. If you don't want to mine, then yes, you'll have to purchase the altcoins on an exchange.
Can a wallet hold anything but BTC?
Each altcoin has its own wallet. You can download them in their respective announcement threads.
Hope this helps!