The safest option is to go with a reputable firm that has well-trained guides and a proven track record of success. Use the internet to conduct your study. A skilled guide will be able to moderate the rate of climb, do daily medical checks, and respond to any signs of altitude sickness. A well-equipped medical kit should be carried by the guides.
When you increase altitude too rapidly for your body, you get altitude sickness. Slow is always preferable to quick, whether in terms of walking speed or daily elevation gain.