I use boys/mens underwear for my girls when they're in heat. You just purchase the appropriate size for your dog, then put them on backwards and use the convenient hole in the front to put the tail through. Use a sanitary napkin in them and voila! there's no more mess.
I also keep baby wipes on hand so I can do a quick clean-up of my girls before I put the undies on them. Baby wipes are also handy to clean up any spots of blood that may hit the floor before you get the dogs covered. If you have a particularly hairy breed, you may want to take some tiny rubber bands and pull the hair on either side of the vulva away and into little "ponytails". This helps keep it from getting all matted with blood when she's wearing the undies.
It's messy and if your girl is anything like my current intact female, the first heat can be particularly bloody. Keep in mind that males will do anything to get to your female and females will often cooperate by trying to get to the males. There are documented cases of dogs breeding THROUGH a chain-link fence and going over or through fences of nearly any height, so it's not safe to leave her out at all without a person standing right there to keep an eye on her. She needs to be 100% confined.
It wouldn't hurt to call your vet and ask how soon you can have her spayed after she comes out of heat. That way if she does connect with a male it won't matter so much. Spaying soon after the heat cycle has ended will not affect her adversely if she's pregnant .. if you wait until the pups are well-developed it would be much worse. But ideally she has no contact with males until she's completely out of heat.
I've had an intact female (not the same dog all the time) for most of the past eight years and have had no problem keeping them away from males, so if you and your family members pay attention it shouldn't be a problem. Making sure your family members understand the risks may be the hardest part! And having your dog go through a heat cycle will probably help you realize how little you want to deal with having an intact dog. I don't enjoy having to clean up after my girls and put the undies on them, but since I show in conformation some I have to keep them intact until I'm through showing.
Good luck, and don't worry too much! Just keep her confined and everything will be fine!
Melanie and the gang in Alaska