I did bit of looking and I would recommend two of
these SD cards.
When you push them in for the first time, you can choose how to use them.
This link tells you how to do it. I suggest that you select to use the cards for extra tablet storage as that is what you need.
That should sort you for quite a while. It is simple to do and relatively cheap.
Yes, you can buy much larger cards if you want, but I suspect you will not need it in the medium term.
If you want to make sure this doesn't happen again for a very loooong time, you can spend more. But I'm not sure you will use it.
This one is twice the size of the first one.
This one is 4 times the size. You can see the relative prices. This last one is the largest your fire tab will accept (documented), so it depends on you. More cost, more time, if ever, that it runs out.
For anyone else who is comparing, I have chosen specific SanDisk mid high range performance. I don't trust Samsung and non branded is a risk which I've been bitten with before.
There are more expensive Ultra options but I don't believe that the fire tablet will ever use the performance.