These are some basic pieces of equipment that are relatively inexpensive and can allow you to successfully work on your fitness from home:
Stability ball (the big one)
Resistance bands (both the kind with handles and the loop ones for monster walks)
Any kind of weights! Dumbbells are preferable over barbells because they’re more versatile.
These next few things are not necessary but can add an extra element to home workouts. They require a bigger investment: