Students often say they would love to do more yoga at home but cannot remember what postures to do. Practicing on your own gives you a different insight into your body than practicing in a class, and in my opinion both have their benefits. Physical yoga practice uses the breath to unite the body and the mind during movement. It allows us to feel more comfortable in a body that may be tense with stress, lifestyle or injury. Breathing practices (pranayama) are advised to be treated with caution as they each have energetic impact on the body. I would advise asking your yoga teacher for advise on which practice may suit you. Working with Ujjayi breathing throughout the physical practice is a great start to working more deeply with the breath. See here for more details.
I would suggest that when practicing alone you try to include all movements of the spine, paying attention to sensations. This would include a side bend, a twist, a forward bend and a gentle back bend. You could include all of these with a lying twist, cat/cow stretches (a forward and backward movement of the spine) and a standing side stretch. Generally lying and kneeling postures are easier on the body so I prefer to start with these to allow my body to warm up and my mind to settle into focus on the practice. The sun salutation can be a simple sequence to remember and a great way to learn to coordinate your movement and your breath. However it can also be a little too intense for some bodies, or maybe some of our bodies need a little more warming up first. Personally I prefer the kneeling sun salutation out of the many variations, and it is fine to adapt the sequence to accommodate injury, mood or time available. Use your practice to find time and space for you and to unwind your body from common postures like sitting, driving or asymmetrical sports.
Different yoga traditions and styles may suggest starting or closing your practice with a breathing practice. Maybe start with Ujjayi and a few minutes sitting or lying focusing on your breath, your body and the present moment. Then move in a smooth, breath focused way throughout your practice. Enjoying and exploring your body.
Most importantly find and develop a yoga practice that you enjoy so that you continue to make time for you.