There are styles of Karate that have gone out of their way to practice with hard contact and which spar regularly, and there are those which have not. Typically, the style of Kyokushin and its offshoots are the ones which do this. While there are other styles where individual schools do train with resistance, that is far more rare. Some are directing you that way, and that is good.
Having said that, I honestly believe that, if you were to find a traditional Okinawan Karate school that
does train with full speed and resistance, that would serve you well from a fighting perspective regardless of what system it is (Goju, Wado, Shorin, Shotokan, etc.). The hard part is finding that.
If "hard contact" is what you are looking for, and from your posts it sounds as if it is, I would suggest seeing if there are any schools from Kyokushin or any of the offshoots of that style in your area (Enshin, Ashihara, etc.). If not, then take a look at individual schools from other styles and ask about sparring, contact, etc. There are even branches within Kyokushin, and some, such as
Kuokushin-Kan have worked to get head punches, etc. back into the curriculum and in their training, which from a self-defense thing is obviously smart.
Kyokushin-Kan USA list of their new dojos! - Time to be United!
North America | Branches | IKO Kyokushinkaikan
If you find someone who teaches Shotokan that happens to seek out training with the
Machidas, that might be a good fit as well.
In addition, some of the advice you have been given is good. Check out schools. Are you comfortable there? What is their focus? Is the distance of travel reasonable for you to get there a few days a week? Is their pricing reasonable for you? Does their schedule fit well into your schedule? Can the instructor teach?
So, of those things that other people are mentioning ARE important, so I don't discount them. But, the other things
you mentioned are valid concerns as well, so don't let people talk you out of what you are interested in.
- If their schedule, location, atmosphere, pricing, etc. is perfect but the system or training method is not what you are looking for, you aren't going to be happy there.
- If the style and training method is perfect for what you are after, but you can't afford it, or can't get there often, or if they are a bunch of jerks, then you aren't going to stick around anyway.
Where are you located? That might make it easier for people to help you.