What do you mean when you say it needs to work with your current phone? Do you mean that you also want to access your Gmail, Google Drive, etc. on the tablet, the same as you would on your phone? You don't sync a tablet to the phone -- you sync the tablet to your Google account, thereby accessing the same information that your phone can see as well. You can install a lot of the same apps on your tablet, but not necessarily all of them, depending on the app.
This is important to know, because since it sounds like you're an Amazon customer, the Fire HD tablets may be a good choice. But Amazon devices don't give you access to Google apps. Midrange tablets include Samsung's Tab A series, which are decent, but they often only come with 16 GB if Internal Storage (which can get used up relatively quickly these days by apps). An SD slot doesn't help to expand app installation capacity.
You could consider one of Samsung's prior flagship tablets, like the Tab S2, which you can get for around $250 these days. Lenovo, ASUS, and Acer also make some decent budget-to-midrange devices.
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