Aloha! Here are some terrific options for your home gym set up.
BEGINNERS: If you're brand new to fitness and lifting weights, I recommend the following: Men: get 10 lbs, 15 lbs. and 20 lbs. Women: get 5 lbs., 8 lbs., and 10 lbs The difference is the colored weights come in pairs, the black hex chrome weight are sold separately. The colorful ones are fun & functional; the black ones give a more professional health club look and feel. Both are great options.
Gym Mat: I highly recommended quality flooring instead of a yoga mat. Why? Yoga mats slip and crease and fold. It's best to have a flooring set up that you leave up. You will be more likely to workout regularly if it's set up as opposed to having to get it out of the closet and set up your home gym. Even a small designated space that is set up is better than a larger one that you have to arrange every time.
I recommend the 1 piece flooring over tiles (the item on the left below). If you are putting flooring over carpet, you must do 1 piece, as the tiles will lift. If it's going on hard surface, tiles will work but I still prefer 1 piece flooring.
Weight Bench: The next item you should add is a weight bench. An adjustable bench is best because it gives you most variety to do more exercises from different angles. If you're budget only allows for a flat bench, that is good too! Its still better and safer than a household chair.
Bands & Balls: These are cost effective pieces of equipment to take your fitness to next level training. They add variety and allow you to use your muscles differently.
Slam Balls: for slamming and weight training. Women: 10 lbs. to start. Men: 15-20 lbs. to start.
Wall Balls: for bouncing off walls, targets, passing, weight training options. Women: 8 lbs. Men: 15 lbs. Start light, the larger size makes it harder to lift.
Jump Ropes & More: I love weighted jump ropes. Why? They are easier to revolve esp. if you haven't jumped in a while. Meaning, less tripping And the added weight strengthens your shoulder while you jump. Women: 2.0 lbs. Men: 2.8lbs.
Bosu Trainer: Good for agility training & a variety of strength exercises. Variety of colors too!