World of Warcraft account - From Free Edition to Paid

Yes, you can keep playing World of Warcraft with your existing trial characters after paying for a subscription. You won't lose any progress. Just note that if you ever decide to not renew your sub, once it expires you won't be able to play any of your characters that are level 21 or higher.

As Nzall has already pointed out, you can continue playing with the same characters after subscribing. From the website:

When you're ready to progress further, simply subscribe to access an ever-growing universe and continue leveling to 50.

Note that you can only play characters over level 20 if you have an active subscription. If your subscription ends or lapses, you would need to reactivate to continue playing as any character over level 20.