My question is about ICO wallets. when participating in an ICO do i need to download a specific wallet for that new coin?
You need to use a wallet for which you and only you have full control of the private key.
A "wallet" is not a great name for an ethereum address, it is a hold over from when there was only one coin, bitcoin.
"Wallet" is just an analogy and its not a good one for etherum.
Everything in etherum is built around signed transactions. Your private key allows you and only you to sign transactions. You can think of it as a mathamagical rubber stamp.
You can think of an ERC20 as a checkbook from the bank of that token. Anyone can write anything they want in a checkbook, but it isn't worth anything until its signed.
If you can sign transactions you can send ERC20 tokens.
Hardware wallets are your best bet. Failing that you might try installing https://brave.com/ where metamask is a builtin plugin.
You can send tokens via https://www.myetherwallet.com/
As an aside, you can think of your public address as a official letter head its public and for everyone to see, but it isn't worth anything without your private signature.
Never share your private key!