Some thoughts. First use your fan every time. If the fan noise is an issue upgrade to a low noise high performance fan.
Next what do you use your gas stove for? If most of the use is cooking rice or making tea, slow cooking a meal…an electric appliance might be great. Spend a week noting when you use gas for cooking. If say 80% can be replaced with easy to use electric appliances then consider the purchase.
In closing use the exhaust fan when cooking with gas as that is for your health.