If you're going to workout at home, there are many things you can do with just your body weight. However, if you want to expand the amount of exercises here are a few recommendations for home equipment:
1. stability ball
2. resistance bands
3. power blocks, or individual dumbbells
4. Trx straps
5. exercise bike
7. Bosu balance trainer
There are many equipment options however these are recommended for ease of use, affordability, and versatility. If you're going to be traveling the number one recommendation would be the resistance bands. They are light weight and easy to store and able to be used for many body parts.