You can buy your own 2-cycle earth auger plus auger for under $300.
Here's just the power head from Northern Tool. You can also buy from local box stores if you have them like Home Depot and Lowes.
Or you can just rent one as drcoastline suggested.
You can build the fence using pre-fabbed sections - usually made in 8' lengths...or buy the lumber yourself.
Either way you'll want the 2-cycle auger and 4x4's for the posts.
Bunch of videos on You Tube that might help. Not hard to do if you are handy with tools. I did mine over 10 years ago - no concrete in post holes - and my fence is still holding up.
My suggestion is to use deck screws (& star bit) for fasteners instead of nails. Easier to use and hold up better.