DO NOT leave your funds on an exchange to send out to the ICO from there, unless that exchange also gives you control of the private keys for signing. Plus you may have to deal with delays.
there are plenty of reputable software based wallets you can use. armory and electrum are some good ones. buy your BTC and send them to a wallet YOU control, and when the ICO kicks off send them yourself from your own wallet.
Spot on with forkedchain. If you dont want to install a wallet on your computer, you can get a wallet through Coinbase. However if you purchase bitcoin or ethereum it will take 5-7 days to go into your account unless you buy with a debit card(higher fees). If you need bitcoin immediately, try changelly or similar sites.