i did - i had some in a wallet and they raped me when i moved it - fees for this, fees for that - can't do anything for free - i shouldn't have to deal with that
and why should i have to pay $150 for a cold storage wallet?
i feel like i should be able to leave it on an exchange and not worry about it - especially one as big as Coinbase
You don't... I've never paid anything for a wallet. Metamask is the most common, it's a browser extension. It depends on the network though. Like I said, there is a learning curve to understand how it all works. I've never owned a hardware wallet (what you probably mean by "cold storage"). But for example, for my ATOM, I have a Keplr wallet. For SOL, a Phantom wallet. For most everything else, Metamask. MATIC goes in Metamask, after you connect it to the Polygon network. It comes "out of the box" connected to the Ethereum network.
Anything on the Ethereum network costs money to transfer, because that's how ETH works (and why it's a dinosaur). But pretty much any other chain costs pennies to transfer.
You're probably good with Coinbase... but the only way to be sure is to move it off an exchange. Then it's only in your control. Any crypto on an exchange, you don't actually own, you only own it on "paper", but it's in their wallet, and if something happens, you could be screwed. Basically all the crypto on exchanges is in their wallet, and they have internal algorithms that allot X amount to Y account, until you withdraw it, it's not really yours.
It's worth spending a couple of days to learn about how crypto actually works.