Jump Rope-one of the easiest and cheapest pieces of workout equipment for cardio intervals
Resistance Bands-another one of the less expensive items that works so well in small spaces and for all ability levels. Check for these on sale during the new year even at places like TJMaxx and Marshalls
TRX would be AMAZING to have at home for total body strength training and cardio intervals--its totally worth the price!!! Its easy to take down and pack in your suitcase for travel, a change of scenery outdoors, and is easily adjustable for everyone to use!
Free weights/dumbbells-Check out places like Play It Again Sports for used equipment you can disinfect and use at home! I'd start with a heavy and a light set. A set of maybe 5lbs and then a set of 10 or 15lbs should get you the resistance you need for most exercises.
Yoga Mat for floor work and stretches
Nice to Haves/Add Ons:
Kettlebells-One of the best pieces of equipment for building strength and endurance. Kettlebells can do everything you would with a dumbbell plus dynamic movements such as swings, clean and presses, etc. More expensive but well worth it!
Agility Ladder--could also use chalk on your sidewalk or driveway! These are great for agility and cardio intervals.
Furniture Gliders-I have a set from Lowes from when we moved that have both a smooth bottom and a furry slip on that I could use on the hardwood floors too! These are great for mountain climbers, push up variations, plank variations, lunges, hamstring curls and more!
Medicine Ball: these are available in a variety of weights, try one in the 6-8 lb range for all around use. You can use these for core work, push up variations, plank variations and cardio intervals.