Is there a cost to open a wallet?

There is no cost to open a wallet.  There is be a small transaction fee to convert USD to crypto and buy the crypto, but that's it.  This is called "gas fees."  You will also encounter gas fees while buying an NFT or listing an NFT.

Coinbase account process (or any wallet process) is also subject to whatever traffic is “on-chain” at any given time.  So if you hit a high traffic time period, with a lot of congestion, fees can go up.  In that case, just be patient and wait for then to go back down...the difference from a night to the next morning can be vast.

Sometimes gas fees can change within seconds.  During signup, you will often have to re-submit transactions more than once, as the market changes so fast that even if you delay for seconds while making a purchase, you'll have to re-run it due to a change in cost.  

When you wallet is open, we generally advise that users buy some BTC and some ETH.  BTC is the first chain and Bitcoin, its currency, is still considered in 2022 one of the most stable in the world.  ETH is a good secondary—this is the currency for the Ethereum chain.  You will need ETH to buy an NFT, for example.  You cannot buy NFTs using BTC.  We also recommend you get at least $100 of BTC and $150 of ETH.  Gas fees can sometimes be high and you want to make sure you have a base amount of some standard currency and enough to buy at least one NFT to get started.