The two most likely scenarios are that you either had malware on your computer/phone that stole your private keys and was able to spend them on your behalf, Or you used easily guessable brain wallet seed. Brain wallets use easy to remember list of words or a phrase. The problem is that if it is not done correctly, then anybody can guess random phrases and check to see if they generate a bitcoin address that has any unspent amount. There are many individuals out on the net that are attempting to brute force brain wallets.

Depending on how much cost/hassle you are willing to put up with, there are many different ways to secure your Bitcoins. You can have an offline pc that you use to hold your coins in cold storage. Only keep daily spend amounts on your hot wallet (the coins on your phone or computer that you are going to use in daily transactions and can afford to lose). You can buy a dedicated device that handles all the security of your coins. These are called hardware wallets. A popular one is called Trezor. With a hardware wallet you are able to store your Bitcoins in a safe offline device. And when you need to spend them, you hook it up to your computer and use it to verify how much you want to spend and to were. The device keeps you secure even if your machine is infected with malware since it never lets the private keys leave the hardware wallet (you steal those you can spend your coins).

A low cost way to have cold storage is creating a paper wallet. A paper wallet is a print out of your private keys, commonly they also include a qr code version of your keys so you can quickly import it into a phone or computer wallet without having to type out the long keys. Just make sure you keep the paper in a safe place and you treat it like cash

I am going to second the malware idea. You didn't just make that transaction by accident.

To stop this in the future is easy:

Step 1. Buy a cheap used Android for under $50. Factory reset it and/or flash the OS if you are comfortable with that level of technical stuff.

Step 2. Download a wallet generator app on it. Generate a new key pair and put the phone in airplane mode.

Step 3. Next time you buy Bitcoin, transfer the bulk of your purchase to that wallet. Now, malware or not, most of your coins are safe. When you need to spend, just buy more coins and repeat. You can just sweep the wallet you made if there are any issues.

Since you know that phone has been flashed or factory reset, it should be malware free. And if it's in airplane mode, malware can't get off of it to report a key.

Sorry you lost your $300 :(

Also clean your PC as soon as possible, or take it to a store if necessary.

Only with the information you have provided, there will be a lot of guess working in order to pinpoint what really happen. The question that we could help you is how to prevent this to happen again. In that case, my only suggestion is to use an offline wallet.

The main advantage of an offline wallet is that your private key would never be in contact with an online computer. Very simple!