Cryptocurrency Primer: Wallet Strategy

Your second wallet should be created manually, not connected with Coinbase.  Naturally, it will be more complicated.  Ideally the second wallet will be set up as "cold storage" so that you don't have it connected to the internet (for security purposes).  

Prefer the feeling of paper money, something you can get your hands on? There is a solution for you. It is possible to print out your wallet keys, laminate, and store under your mattress, for example: Creating Cold Storage Using a Paper Wallet

You should review some guides about bitcoin storage, hot vs. cold wallets, etc.  

You can either buy a "hardware wallet" like a Trezor or Ledger or create your own using a USB flash drive.  

Wallet Software

It looks like "Electrum" and "Exodus" are the popular Wallet software names.  

DIY: How to create an Inexpensive Bitcoin Wallet USB Thumb Drive

This is not investment advice

For those who are interested in the underlying technology behind cryptocurrency and the software behind it, based on this series of articles, anyone can easily create their own "Coin" (like Dogecoin).

The reason Bitcoin has risen to over $40,000 is simply because people have decided to put their faith in it.

Personally, I believe that Bitcoin has the potential to properly store value. Its downfall is that it won't work well for rapid transactions, meaning it probably won't be able to replace something like Visa/Mastercard, as I understand it.