I have always like to use kunai and katana, but now I finally want to learn how to use the katana properly. Are there any that would be able to pair it with hand and feet fighting as well?
There are several different martial arts styles the practice swordwork with the katana. If you're looking to do sports sparring, I'd advise Kendo. If you're looking for something closer to historical teaching, and with unarmed combat mixed in, you're looking for Kenjutsu. That is sometimes taught on its own, and is sometimes part of another style such as Jujitsu or Bujinkan. Lastly, as Philip Klöcking pointed out in the comments, there is also Iaidō, which is essentially the art of drawing the sword, striking, and then resheathing it in one fluid movement. However, it is very tightly focused on just that practice, so I would probably not include it in a list for sparring.
In all counts, you are likely to face one of the pitfalls of Traditional Martial Arts in general, that what you are being taught is largely traditional movements that are not tested at speed or with a resisting opponent, or if they are, it is generally within a rigid set of guidelines (Kendo, I believe, has a limited set of "valid" strikes that will count toward your score) and only against people who train the same style. If that's enough for you, that's perfectly fine. The odds of you having to use a sword in real-life are miniscule.
This should just be a comment under Macaco Brancos answer, but my reputation is to low. So I write it as a full answer:
In your own comment, you write that you think about learning Ju Jutsu. It will probably depend on the style and your teacher, but in 3 years of training I never even held a sword. When using weapons we never even consider anything beyond sticks and knifes.