To build a Crypto Wallet like Coinbase you need to integrate and setup all the coins you intend to support. The more coins you integrate , the more developers and server costs you will have.
Using Crypto APIs, you can start with any of the supported protocols at once and rely that Crypto APIs is going to add new protocols all the time.
Using Blockchain API, you can generate a hot wallet for each user, get a notification for all wallet events, auto forward the funds to a cold wallet, check the balance, check wallet transactions, etc.
Using Crypto Market Data API, you can get cryptocurrencies and FIAT current prices.