New York is probably very different than where I am in Arizona. I was able to get 2 acres for $1,200, of which $200 was various documentation and closing fees. I received a title from the county. My area is zoned residential/agricultural, so I can live on it in an RV.
One piece of land I looked at wanted $700 for title insurance on 2.36 acres of land selling for $600. So they wanted more for the title insurance (which pays you for the value of the purchase if there is a problem with the title that interferes with your ownership of the property, meaning they wanted $700 in title insurance to protect a $600 asset). However, in other cases title insurance can be worth it, just consider the cost of it with the value of the land title it insures (I'm guessing land in upstate New York is a lot higher than in Arizona, so title insurance might make sense there).
I found the clearing difficulty depends on what you want to build. I have to keep my structures under 120 sq feet so they don't need permits. I don't have trees to deal with like you do, where I am the main issues is leveling an area to build on and planning for flash flooding. The challenges are likely different where you are.
For power, I've lived out here with as little as 60 watts feeding a 15 amp hour battery, but now I have 800 watts feeding a pair of 125 amp hour solar deep cycle batteries. It keeps my net connection up, laptop and phone charged, and depending on time of year about 8 hours of x-box and tv. This summer I'll be adding 1080 Watts into a 100 amp hour battery that will feed a small 115v/5amp air conditioner, but that luxury will be about $3,000 with inverter, cabling, etc.
A 1.7 liter AC/DC non-compressor fridge will draw about an amp. I use hauled water, a decent 250 gallon container is about $125. My plan is for rain catcher by next winter, but I will have to put up several to be self-sustaining and my water usage is quite Spartan.
What I learned is that you have to be able to live on the land from day one if you're going to stay there and develop it yourself. My solution to that was an ultra-cheap RV, solar power and hauled water. I recently fenced off about a quarter of my property, and will be putting in a chicken coop this Spring.
So far, the cops haven't had a problem with me being out here, they've been by twice (separated by several months) and their main interest seemed to be making sure I wasn't going to hurt myself and I wasn't pulling a Walter White. After they satisfied that curiosity, we mostly just chatted about 12-18V tech for a while.
I hope for great success for you. Watching the land change, little by little, into your vision is something worth developing patience for. May the spirit of the land somewhere call to you, and may you find home.