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Dumbbells
I recommend having at least two sets of dumbbells - a heavier and lighter set. Range 5-20lbs.
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Mini Loop Band
We use these from time to time - I recommend a variety pack, or a medium strength one.
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Yoga Mat
This is my favorite yoga mat, but it is an investment. Not mandatory.
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Workout Bench
We use a bench from time to time - not mandatory, but nice to have
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Dowel
58 inches - or just go to HomeDepot and get a similar size dowel.
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Weight Rack
This is a great set and keeps the dumbbells organized in your space.