As you would expect there are a lot of factors that go into deciding which LEO orbit is most suitable for a satellite. I'm going to describe the case of a single satellite here but it's worth noting that constellations of multiple satellites get even more complicated again. Taking the GPS constellation for example, the orbit planes, phasing and height were all optimised to ensure at least 4 satellites will be in view anywhere on the planet at all times. That's not a trivial thing to work out. Your right in saying that drag is an issue, but is generally means people ignore anything below around 400km, there is a lot more to choosing the exact orbit altitude and inclination.
Going back to a single satellite, it all depends on what your satellite is going to do and where your ground stations are located. Most LEO satellites are used for earth observation and in vast majority of cases they want to image the whole planet. This means that they need to be in a polar orbit because lower inclination orbits never pass over the poles so would not be able to image these areas. Often a special type of polar orbit will be used which is sun synchronous, the plane of these orbits remains fixed relative to the position of the sun. They can be used to ensure your satellite will always be passing over the earth at a certain time of day, dawn/dusk or example. Or about 2-3 hours before or after noon which is favoured by spy satellites because the angle of sun at this time is ideal for showing the shape of buildings in shadows. Sun synchronous orbits enforce a mathematical relationship between the orbits inclination and height, so if you know your satellite needs to orbit at 500km then the exact inclination of your orbit is then fixed.
The orbital height of earth observation satellites is often chosen to produce the best resolution possible while ensuring good global coverage and revisit times. For example if your satellite has a camera with a 30 degree field of view, then it can image a strip of the earth as it orbits overhead. The higher its orbit the greater this 'swath' width is but the lower its resolution, so the lowest orbit possible is chosen to increase this resolution. However you probably also want the swath of one orbit to overlap with the swath of the next orbit so that you can image the whole earth every 12 hours, this means there is a limit to how low your satellite can orbit before the image strips no longer overlap. These relationships are used to determine the orbit height and inclination of many earth observation satellites, and are often driving by the imaging playload.
All satellites including comms and earth observation need to communicate with ground stations on the earth, these ground stations could be your customers or the main station you use to command your satellite. The amount of time and how often your satellite is in contact with ground stations if often a critical part of choosing your orbit. It's also a reason why there is small Norwegian island called Svalvard which has a huge cluster of ground stations due its close proximity to the north pole, polar orbits with a ground station near one of the poles allow for the most frequent satellite contacts using a single ground station (equatorial orbits aside which are useless for almost any satellite).
The ISS is a notable exception to these ideas, due to the huge mass which needed to be lofted and the political collaboration between Russia and the US its orbital inclination was chosen to be half way between the ideal inclinations for Cape Canaveral in the US and the Baikonur Cosmodrome in Kazakhstan. This made cargo and crew launches possible for both countries.
Finally most small satellites piggy back on larger launches so generally don't get much say in what orbit they end up in. This is case for missions from the Surrey Space centre where I work, this means that we get relatively few ground station passes over our UK site, but that's what you get for cheap launches.
Hope this gives you a bit of an idea what goes into choosing a LEO orbit.