This site has the most comprehensive and easy to follow instructions for making sauerkraut I've ever seen. She covers virtually everything you might want or need to know. You can absolutely make perfect sauerkraut by following these instructions. This is not hard or involved, and it doesn't take all day like canning does.
I only want to add a few comments. You can make just plain sauerkraut with salt and cabbage only (duh) and not add the carrots or dill if you don't want to. I add garlic and dill weed, but you may prefer plain.
When you get to step 5 (submerge and seal), if you're using the pickle pusher (which is the easiest and most reliable in my opinion), just insert it. You don't have to worry about covering the kraut with a cabbage leaf or dealing with floaties this way.
You can taste-test it after 4-5 days. It won't hurt to open the jar, remove the weight and get a bit out to taste. If it tastes like you want it, pull the weight out, put another lid on and refrigerate it. I think it tastes better after at least a couple of weeks. And if everything is proceeding well, it can go longer. The longer it goes, the more tart it will get.
I really would like to encourage you guys to make ferments. They are so good for you.