The big advantage is that you can tailor to your kids needs and interest. I dislike the term home school because its not like school, and its not all done at home. Doing school at home is IMO combining the worst of both.
Maths and English (assuming you are in an anglophone country) are important because you need them for other things. You can make them fun and not involve too much study. Reading for pleasure, maths fro and of games, all sorts of things. You need far fewer hours of studying to learn the same amount so do not aim for school like hours.
Encourage self-discipline and motivation. This really pays off in the long term. Have confidence and feel your way. You need to spend a lot of time with them, not teaching but guiding, encouraging, and knowing where they are. I am also love conversational learning.
Until they need to study for exams avoid a fixed curriculum. Do lots of hands on stuff. We made circuits and soldered things, had lots of hobbies and activities. One of my favourite stories is that a senior electronic engineer worried about whether universities neglected practical skills asked a room full of junior ones when they first held a soldering iron and my daughters answer of at the age of eight startled everyone.
Its a bit easier in the UK because home educated kids can sit the same exams as everyone else at 16 (which is the end of compulsory school here). My kids then went to a sixth form college to do A levels. You need to think about paths to qualifications and university. As they get older courses tutors and exams can get expensive but a lot cheaper than a fee paying school.