Climbing harnesses are made in different sizes and shapes with different amounts of padding. It's worth going to your local shop and trying some on rather than ordering online, if you can.
Select a few climbing harnesses that fit correctly, then hang in them. Good shops will have a facility for you to do this. It won’t be super comfortable, but the leg loops should hold most of your weight, with the waist belt supporting your upper body so you don’t tip upside-down.
Try a harness on with the waist belt around the smallest part of your waist, above your hips.
The harness needs to go small enough to be tight over a t-shirt, with enough adjustment to get it on easily or wear a jacket underneath too.
Some climbing harnesses have adjustable leg loops too. This is useful if you plan on climbing in cold environments where you'll need to wear thicker pants, or if the fixed size options just don't quite fit. The leg loops should fit closely around your thighs without hindering movement.
Climbing Harnesses: The Rise
The 'rise' is the distance between the waist belt and leg loops. Think of it as the measurement between your belly button and crotch. Women's harnesses tend to have a bigger rise, to fit women's body shapes better.
If the rise is too short, you won't be able to get the waist belt all the way up to the smallest part of your waist.