Hello /out/ismos.

I've recently started camping during my weekends in the Adirondacks
I've realized that my gear is terrible insufficient, I've gotten by on Walmart brand OT knives

I have come to the conclusion that for splitting wood and other camping activities, I need something better.

What knife or hatchet would would best for my applications under $150?
What makes one more useful than the other?
Any case for both?

Thanks!