Is it better to workout hard if you have an increased heart rate? For example, my heart rate is 120 bpm normal range is 80-100, what workout?

What workout is right for you depends on things you don't tell us.

What is your goal? Is it overall health? Fitness? Weight loss? Cardiovascular endurance? Getting better at a particular sport or activity?

How often can you work out? It's pretty difficult to do a high-intensity workout if you can't do it at least every other day. But you can pick up a low-intensity workout and do just fine even if your schedule is irregular.

How much time have you got, including getting to the place you work out, cleaning up, and getting home after? That sounds unimportant until you factor in that working out means you have to shampoo and style your long hair, for instance, or drive to a gym that's 40 minutes each way.

There is no single "better." It's what's better for you--including how likely you are to keep doing it.