I have never tested the mobile app but I don't see anywhere in the site that says you can buy bitcoin from them or their partner using credit cards

https://blockchain.info/wallet/#/What do you use as a wallet if i may ask?
Wallets are used for storing your Bitcoin. The are many different types of wallets. Blockchain.info is an online wallet which isn't the best choice if you are going to keep a bigger amount of money there. The best wallets are these which allows you to control your own private keys (proof that you are the owner of certain coins). If you don't want to spend extra money on a hardware wallet which are one of the most secure methods to store your BTC, you should consider using Electrum (free software which allows you to control private keys which I would recommend you to encrypt with for example VeraCrypt) or create a paper wallet, it's not as convenient in use as a hardware wallet but it doesn't cost anything!