You will need to purchase a monthly subscription. You may also need to "purchase" the free trial, but I am unsure about that. I know you can continue playing your free trial. Go to the character log in screen. There should be something about account info/billing there (under options)
You will definitely need to buy the Catacombs and DR expansions (29.99) if you want to get those. The monthly fee is not higher for having these two expansions, so that would be a one time cost.
If you have a gaming outlet near you, you might just want to go buy the Epic Edition of the game. It will be all you need, and includes the Cata and DR expansions (you will still need to subbscribe for a monthly account), but the most it will cost is the same 29.99, and i have heard people getting it for less than that (so it may even be cheaper than you having to pay for the two expansions). this would mean losing your characters you created so far, but if you are not too far along, this may be easier in the long run.
Up to you though, can do it either way.