Does it make sense to use filters for black and white photography, as opposed to using software to convert photos? As I understand it, photos that have been made in a natural way (using filters) are more highly regarded than ones converted in software? What can I do by using filters, and what can I not do by using a software converter?
Photos made "in the natural way" may be more highly regarded by some, but that alone is no reason to go out and buy a set of filters. There some genuine advantages to working this way, however.
For example filtering the light before it enters the camera can prevent overexposure (and hence loss of detail) of one ore more colour channels. This can be important if a scene is dominated by one colour of light that you want to filter out, you could do it in post but to gain the correct exposure for the other channels you might end up massively overexposing one channel which can result in flare, loss of contrast, or sensor bloom.
If you are serious about black and white photography, you might want to use a camera optimized for such exposure - having a monochrome sensor without Bayer filter. The upside of such sensor is that you won't have a color filter throwing away most of light in front of each pixel, resulting in better sensitivity, resolution, and signal to noise ratio. A consequence is that color information will not be recorded, so with such sensor you cannot apply color filters in post - you have to use physical ones during exposure.
However, most people won't invest into a special body for black and white photography; in such case, shooting without filters and applying filters in post gives much more control over end result. As usually, the price for the flexibility is the time it takes to get a finished image. For 99% of cases, using a physical filter will not give any significant improvement in end result over what's achievable in post production.
Shoot your B/W images in color and then use Photoshop's channel mixer to convert to B/W. This allows you to choose the exact effect of using a colored filter in front of the lens after you've made the shot
What I have found in addition: There is a plug-in for Photoshop or it can be done manually without it by using those editor itself. Other question: every filter costs $10-15 x (red + blue + green + yellow + orange) = $50-75. Photoshops costs more.