How strenuous does my workout have to be?
The answer really depends on you - your health, your short-term and long-term goals.
If you're exercising to improve your heart, lungs, and overall health your workout doesn't need to be strenuous. You should do a cardiovascular exercise that you enjoy at a moderate pace and some strength training to increase bone density and help you function every day at your best.
If you're exercising to lose weight (in addition to all the great health benefits) you need to push yourself. You need to lift heavy enough weights to challenge yourself at least twice a week (or do a comparable strength training routine such as yoga or Pilates). You must do effective cardio (and a variety of cardio) and make sure to include intervals twice a week (speed up and slow down to challenge your body).
The truth is if you don't challenge your body it will not improve. Obviously you don't want to injure yourself or push hard if you have health or joint issues, but if you are a healthy, motivated individual who is trying to lose weight you should be a bit sore the day after a workout and you should be tired after you exercise.
It's okay to work hard. Working hard is the key to success.