When my husband and I bought our property, we scrounged up every penny we could for the downpayment, including cash advances on low interest credit cards. Then we got a line of credit for the rest. We spent another year at our rented place while my husband finished his degree, then we moved into a tent on the land. I don't remember how much money we had at that point, but it was less than $5,000.
Neither of us had jobs and since we didn't want to live in a tent over winter, we spent the summer and fall just building our house. That meant living on credit cards. We probably had $20,000 of so of credit card debt from building the house and living expenses for six or seven months.
Neither of us works in high paying jobs, so $20,000-$30,000 combined income was normal for the first few years. We paid off the credit cards and line of credit for the property in less than five years because our living expenses could be so low. Not having to pay rent was the big one.
Getting land is the hard part, but after that I don't think you need much, if any, money saved. If you have some, it's way nicer and easier, though. Not having any money meant we had to do things like wait until midway through a very cold winter before we could buy insulation for the floor of the house, which was pretty shitty.
So I guess how much money you need to save depends on how much comfort you need.