I was homeschooled the whole way, and I loved it. I'm in college now, and far more prepared and adaptable than many of my peers.
Is homeschooling ideal? No—I've yet to see a method of raising and educating kids that brings the best results every time. You're going to make mistakes. Things aren't going to be perfect for your kids either way. So why homeschool? My parents gave me a well-rounded education; more so than even most other home schooled kids. I played piano and guitar, sang, learned to paint, read books like crazy, gardened, cooked, baked, taught myself dog training (and actually made a bit of money at it), needlework, horseback riding … those were just the extra-curriculars, of course ;) I aced Chemistry 151 in college, because my high school curriculum was harder. I speak Spanish and a little French. My poems have won awards in college.
Not all homeschoolers are well-adapted, well-socialized people. But of the literally hundreds of homeschooled kids I know, only a handful are the repressed, rule-bound, maladjusted type. Of my homeschool friends who've attended college, not one has failed to adjust, adapt, and function as a "normal" human being.
Do we miss out on some of the things public and private schooled kids do? Yes. Sure, we have homeschool proms and dances, but not as many as others. Yes, we have choir, but it only meets once a week. We have co-ops and sports teams, but again, not as often or as prolific as other schooling methods. And all of these extra-curricular perks vary with location. BUT we also miss out on the drugs, the sex, the abuse, the bullying, etc., that is more of a risk in some public schools (notice I said "more of a risk"—public schools can be as safe as my homeschool environment, and homeschool environments can be as dangerous as some public schools).
As I've entered "real-life", adult life, I've noticed that we really never spend large amounts of time with our peers. The public schooled kids I know, in general, have a harder time adjusting to interactions with "others"—professors, work supervisors, younger friends, mentees, etc. Again, "in general".
In the end, it's all in the way you do it. I know of some really, really great public schools. I know some really atrocious ones, too. I've been in private schools that are more repressive than the majority of homeschools. And there are some really horrible homeschool situations.
But, I plan to homeschool my children, when (hopefully!) I have some of my own. In the meantime, I'm studying to be an English/lit teacher, because I love literature and I want to teach others the love of writing. OP, if you do homeschool, take it one day at a time. That's how my mom did it. She didn't think ahead to the frightening prospect of chemistry and bio lab. She just started at the beginning—teaching us how to read, to count. History and social science were saved until we were 4th or 5th grade, and then we learned such things from biographies and field trips. Her main focus was reading, writing, math. And then we played, we created. My three siblings and I soaked it up, learning more on our own—through supervised, educational play and good books—than we could have through textbooks and tests and lectures. As we approached high school, she mixed in science, pursuing co-ops with retired professors for the "harder" subjects. Except it never seemed harder to us: it was just the next level of learning. And we're good at teaching ourselves. Classrooms with poor teachers haven't bothered me in college, because I'll pick up the book, I'll do the research, and I'll teach myself.
I hope this helps in making your decision :)
“A man can no more diminish God's glory by refusing to worship Him than a lunatic can put out the sun by scribbling the word 'darkness' on the walls of his cell.” CS Lewis