For me, I absolutely needed the maternity pads for about the first week or so and I didn't have especially heavy bleeding or a bad tear. They were just more comfortable and the padding helped when sitting (you'll probably be a little sore). I switched to regular maxi pads (extra long with wings) after that first week.
I had a home birth as well so stocking up was important. I had maybe 1 pack of 20 pads, but definitely needed another 2 packs before I switched to the regular pads. Also, I'm sure you already know it, but get twice as many floor coverings (tarp or shower curtains) and bed pads as you think you might need. I moved around a lot more than I realised I would during my birth and ended up giving birth in my bedroom (even though all our supplies had been set up in the lounge). The carpet took a bit of a hit as a result. It's fine now but I definitely wasn't as prepared as I should have been!