Hi there Newbie!
For starters, I'm sorry to tell you that to my knowledge there really isn't anything mid-range between private and group instruction. The closest you might come is a group class specifically for technique or styling, but the fundamental problem is that a group setting does not function well for teaching/learning technique. (This statement is a bit too broad, so let me elaborate.)
Technical theory can be taught in group classes, and to some extent be correctly assimilated, but the format doesn't allow for much correction of people's inevitable individual problems. Also, the format lacks what is for many the most important method of learning: feel. Anyway, I'm getting sidetracked.
As for instructors teaching out of their homes or coming to yours, both require adequate facilities, which aren't too common. And personally, if I go to someone's home to teach them I actually charge extra, because since I can't schedule lessons back to back I'm losing teaching time.
Finally, while there's nothing wrong with learning a group of patterns to get you started and going out dancing right away, make sure you learn basic lead & follow technique too. You don't have to be an incredible dancer before you start going out and having fun, I just don't want you to be dangerous. I've been led by men who've learned patterns much too advanced for their technical level, and nearly had my wrist broken. Needless to say, that's not fun. (I'm assuming you're a man. If you're a woman, following technique would actually be much more useful to you than patterns.)
If some other resources are out there for you that I don't know about, I'm sure someone else will reply and fill us in. A good, budget-conscious way to go is the combination approach: for example, go to group lessons weekly, and take a supplemental private lesson every other week.
Another idea is to find a teacher who will let you bring in a very small private group (oxymoron) at the private rate or some small additional charge. Then you and whoever you split that time with also split the cost. I've taught several pairs of couples this way, and I can teach them the patterns group-class style, then go back and forth working with them individually. (This works very well for people who want to lower the cost, or who don't like intense focus for an entire hour.)
Whichever way you go, I wish you the best of luck!
-Melissa