It kind of depends on what kind of sparring, and with who. Heavy contact - that's usually a couple of guys who are used to heavy contact sparring and have geared up appropriately for what it is they're doing. And the whole idea of "heavy contact" will be different for beginners, intermediate and advanced.
Cup and a mouthpiece are musts, IMO. After that, it's up to you. As for headgear, my opinion on that has changed so much, and so many times over the years - I really don't know.
I only go the chest protector route when sparring students for the first time. Their first time is always with me. Other than that I'm never wearing a chest protector, because I'm not letting you make me need one, regardless of how skilled you are. That just ain't happening.
Ii haven't, and won't, spar with leg kicks for a long time. If you kick me in the legs - I'll either cry or shoot you after class.
I like to wear shin guards.
Here's the thing - if you can find a sparring partner, a guy you can spar once a week after class, a guy who's as equally nuts as you are, regardless of what that level of nuts is, you're golden. A good way is to spar/roll for one minute after class. Definitely set a timer. Next week is two minutes, then three. And so forth. In a couple years you'll be surprised as to what you have accomplished, not only because of your extra sparring/rolling, but because you're both improving with a couple more years of class instruction under your belt. (and it will make all classes so much easier, and so much more fun than you can even imagine.) One of the greatest enjoyments in the Arts is to have a good sparring partner. if you find that, embrace it for all it's worth, because it's not forever.