The number 1 factor is to choose a gym you'll actually go to. Pick the closest one to where you live. Pick one that's open for as many hours in a day as possible. The fewer excuses you can give yourself for not going, the better.
Decide if you want to do a strength-focussed program or a cardio-focussed program (both can lead to weight loss if accompanied with the correct diet).
If strength-focussed, count how many proper squat racks are in the gym (not smith machines). Ask if the gym allows the use of chalk. A bonus (they're super rare.. might only find this on a university campus), the gym should have an olympic weight-lifting platform with bumper plates and allow dropping of loaded bars.
If cardio-focussed, look for a gym with the largest number of stationary bikes and treadmills.
Regarding the agreement, month-to-month plans are better than yearly contracts. Even if you have the option of a month-to-month plan or a cheaper yearly contract from the same place, pick the month-to-month plan in case you realize you would prefer another gym after a couple of months. The freedom to change is worth the price.
When taking a tour, go at the time that you're most likely to be going to the gym yourself. See how busy it is. Is the equipment you want to use actually available?
(As an aside, I believe your goal of losing 20kg in three months is really ambitious. That's 3.3 pounds per week. If you're going from no activity to an activity level that's going to result in 3.3 pounds of weight loss per week, you'll be toeing a fine line between eating enough to support your body's recovery from exercise and eating a small enough number of calories to allow weight loss. I'd suggest focusing more on eating properly to support recovery and muscle development (even if you're not doing strength training, the cardio will develop muscles), and don't be disappointed with a slower weight loss. Think long term. Injury or exhaustion caused from inadequate recovery and nutrition will set you back much more than losing only 1 pound per week.)