Most if not all martial arts do have strikes to the throat and eyes. Though I wouldn't worry just about those strikes. I would learn from a good teacher that really knows martial arts.
Now you may have heard the term Mcdojo here in this section. If you haven't I will tell you. Mcdojo's also known as dojo huts, or belt mills are martial arts school that most of the time have nothing to do with martial arts. Some times you may learn pretty kicks but nothing really helpful or useful. Now in those mcdojo's the owner will put prices on everything and make the prices insanely high. You have contracts, yearly fees, monthly fees, high testing prices, very high uniform cost, insanely high black belt testing fees, so called leader ship club fees, and many more.
The red line for all of this is children getting black belts. Now if you see people under the age of 16 getting black belts then it is a mcdojo for sure! Even 16 to 17 years olds would be a little wary in my opinion but you should see if they can beat the lower ranks and if they can do well against the older people of the same rank. Also if you see anyone under the rank of 3rd dan black belt teaching class completely by him or herself with no help, then it is most likely a mcdojo as well. Now why I don't agree with children being black belts is because a black belt is a black belt. To be a black belt means you have to be able to defend against other black belts that are adults. Not many 8 years old could do that if any.
So good luck with your training and I hope you find a good school to train at.