We home-schooled our oldest for 10 years, 2nd child for 7 years, and youngest for 4 years. The 2 oldest are girls, youngest a boy. We stopped because my wife had to go back to work.
We were members of a home-school co-op where we paid for courses that our kids took. In our case all of the "teachers" were college graduates. This was in addition to teaching that my wife did at home. The kids ate lunch together, took field trips, and now have sports teams that compete with other independent schools. In a sense "just like regular schools".
Home-schooling requires a commitment, my wife didn't work and curricula are not inexpensive. You can buy "all inclusive" curricula or you can pick and choose to create your own. Educators will tell you that we all have different learning styles, some are auditory, some visual, and some kinesthetic. My wife was a state certified teacher and my middle child is an elementary education major now, so I learned this from them as well as observing my kids. Home-schooling allows some tayloring to your child's learning style.
Our kids were tested annually for academic performance using the ITBS (Iowa Test of Basic Skills). That was what we used as a measure of their academic progress, the test was administered by a third party so we could not influence the results.
Socialization is the issue most often questioned about home-schooling, whether you home-school, send your kids to public or private-schools, they don't grow up in a bubble. Our kids socialized with other kids of all ages through church and sports activities. There is an unfortunate perception, unfair, that people home-school to isolate their kids, I'm sure some do, just an unfair generalization, and generalizations generally aren't worth a damn. My question is what about bullying, it's going to happen, that's part of socialization too, but we sure don't our kids to give or take it. Aren't gangs a "social" institution?
There are "religious" and "non-religious" curricula available, all you have to do is look for it. A home-school conference is a good place to start, they usually have curricula fairs with vendors set up. You will see some "typical" home-schoolers and some that will shock you.
My kids survived home-schooling, public school, and public colleges. They all three work, gained entrance to their colleges of choice, and have done well academically.
I looked at it this way, we invested by choice in our kids, I don't expect everybody to do it. We had some negative experiences and a lot of positive. It is a decision you have to make together. It forced us to be conscious of learning opportunities.
Home-schooling laws vary by state, so you'll want to check with a state home-schooling association before you start. You'll have to let the local school district know what you're doing as well.
Sorry to ramble and I'm sure I have made some grammatical errors, but that's my 2 cents worth.