JFK Airport to a hotel in NJ, Newark with my luggage? How to get there cost effectively and easily?

ETS and All County Express have direct JFK-EWR shuttles for ~30 USD and your hotel is almost guaranteed to have a free shuttle from EWR. This is not the absolute cheapest but certainly the most convenient. It might take a long time, these are shared services. I doubt there's a shared shuttle from JFK to anything in Clark but you can try entering your hotel in either and see whether you get a shared offer, checking costs nothing.

You could save some money by taking public transit but the savings will be low, you will need two transfers and at the end might not be anywhere near close where you want to be as there is only one stop in Clark (well, two, but no bus stops at both!) and altogether it's just not nice. I will not recommend someone off a 12 hour plane ride to transit at the hellhole called Port Authority. If you want to experience it, sleep first. And you will experience it if you manage to take public transit from Clark into Manhattan, your bus is 112 and arrives to Port Authority.

Even if you end up needing to take a cab from EWR it's still a hell lot cheaper to ride ~11 miles from there. Theoretically you could take another shared shuttle from EWR to Clark but I bet you won't want to, 12 hours on a plane, two hours to get to EWR...

Unasked advice: unless you are in Clark, NJ because it's your destination (but why on earth would it be??) or you are going to fly out from EWR the next day, pick a hotel somewhere else. If you are flying from EWR make sure you have a hotel that provides a shuttle to EWR because otherwise you are pretty much stuck. Public transit in Jersey is close to non-existent. As with many other places in the USA, you need a car.