To do the rock gardens, drops, and jumps you’re expecting, you’ll find full suspension is the best answer. There are a few options under $2K, but somewhat limited on selection and options available. More options are available once you get past $2.5K and that’s hard to justify for someone just getting started. For most people starting out with a budget, there are some quality hardtails around $1K. It makes a lot of sense (cents) to go this route, ride it hard for a couple seasons to see what you’re really into, and then think about a major purchase down the road if it sticks. Think about doing a couple rentals to see what works.
A few other suggestions: big fan of 1X gear system (which means no derailleur in the front) and to do the kind of stuff you’re suggesting I strongly recommend a dropper post. If you do go with a hardtail, look for “plus” tires – a little wider (about 2.8″) will suck up smaller roots and rocks nicely.