The great thing about homeschooling is that you can spend as much or as little as you want. I've known people who homeschool practically for free and I've known others who spend a whole lot of money.
I have one 4th grader and we spend $20 a month for an online curriculum and then about $50 a year on a different math curriculum. That's it. In fact, this is the first year we've used the online curriculum. Before that, we'd pretty much piece meal everything together. I would spend $30 here for a history text, $10 there for a writing guide...
Ultimately, you will pay more for the convenience of an actual whole or "boxed" curriculum. It will come with all the books you need as well as calendars and teachers guides. That has never been a financial option for us, and I don't like the rigid feeling of a boxed curriculum. I prefer to be able to work with my kiddo on his level, wherever that might be, and I have found that creating our own curriculum works beautifully for that. Of course it is more work, but it's work that I think is worth it.
But I guess it depends on what you mean by expenses. I buy a lot of games and books for my son, as well as a subscription to Netflix and museum memberships. If I counted that stuff my number would be a lot higher. But I don't really count those because I believe everything we buy is educational, even if it's a new food processor for me, so I only count the "schooly" stuff.
As far as I know, there aren't any scholarships or grant money for homeschooling in New Mexico.
Please feel free to come to a park day. Finding a support network is often the difference between feeling overwhelmed and feeling confident.