I second what others already said: a full single piece, stretchy 3mm, with additional separate hood for when needed (not needed most of the time).
And a good computer, very important is a good display which you can read easily.
I like to have my own fins and mask, which are perfectly suited to the peculiarity of my body. But probbaly you already own these items.
You can survive with rented regulator and BCD: they are decent in most places, and expensive to purchase. But if you make more than 20-30 dives/year, you can consider purchasing them as a good investment.
Most recreational, tropical scuba divers do not need to purchase tanks or weights, you always rent them on site.
Regarding certifications, you generally need OW, AOW and Nitrox. If you are OW, you can get AOW simply diving during your next holidays, and Nitrox is usually an out of water, purely theoretical certification, possibly followed by a single "test" Nitrox dive.
Whilst AOW and Nitrox are not strictly necessary, they allow you to adhere to the diving policies in more varied situations, without the risk of being excluded from what the others are doing.