When I first started writing this I actually had a list of your typical supplies. You know, your art supplies, pattern blocks, and the like. Half-way through, however, I changed my mind. I am getting way ahead of myself. While those are some things that I think would benefit you greatly in your journey, there are a few more important things that I believe every homeschool should have.
1. A Vision or Mission Statement.
As a family(or at least with your spouse) plan a time to sit down and write down why you chose to homeschool. It doesn't have to be formal or fancy, but it should reflect your long term goals for your child's educational and spiritual welfare. Pick a Bible verse (or several!) that encourage you and inspire you. When things get rough or when you feel like you aren't doing a good job, go back to this mission statement and re-read it. You may even chose to hang it in your homeschool space as constant reminding of why you chose to homeschool. If you need help starting your mission statement, feel free to visit mine. It is written formally, but you can write yours however you like!
2. A Great Planner
I know some people who can fly by the seat of their pants and get a lot done, but for the majority of us we need at least a basic plan. I don't neccessarily mean a "we.have.to.do.this." plan, but at least something that sets some goals and helps us keep track of what we have done. I suggest A Well Planned Day. This planner has places for up to 4 different children and includes nifty little encouragements, catechisms, grocery plans, and spaces for keeping track of the budget. At the beginning of each month is a place for goals and at the beginning of each "semester" places for keeping track of attendance and grades. This has been a time saver for me!
3. A Library Card
I honestly do not know how any home functions without a library card; when we check books out it is by the dozen! I know families who have up to 100 books at a time out! The library will save you tons of money on books you would have had to purchase, plus most libraries have educational DVDs and some, like ours, even have "quiet rooms" with a white board and desks for you to do some of your lessons at! Trust me you NEED a library card!
I hope that you will take some time to think about these things and that they encourage you in your homeschooling journey!