As far as I am concerned, the bow is the real instrument. Everything 'musical' (besides vibrato) is performed with the right hand and the bow. Because of that, selecting a bow that is compatible with your cello is of utmost importance. "But what does compatibility mean? Can't I just play my cello with any bow?" Well, you could but it doesn't mean it will be great. Your cello and bow each have a favorite resonant frequency, and finding a match will bring you much better tone, control, vibrato, performance, etc.
When someone comes into our shop to buy a bow, initially, I have them do just 2 things: starting in front of the winding (not too close to the frog, where it can sound scratchy), I ask them to bow the C string, then the G string.
In the video below you can clearly hear the difference between the 1st and 2nd bows, which are not compatible, and the last bow, which IS compatible. The 1st bow barely is able to get the C string moving at all. Listen carefully to it. The 2nd bow is particularly incompatible with the G string and doesn't sound good at all on it. Then listen to the last bow, how the C string starts to make a clear tone immediately.
It is more evident on the 2 lowest strings, and typically results in a hesitancy, stutter, or flutter before getting the string activated. The most important thing to look for is a bow that gets your C and G string going without a lot of effort. That is a sign of compatibility.
So, after finding a selection of compatible bows, then I have the player play something that they are familiar with. Whatever they play is based on their level and experience, with professionals often looking for a bow that they can bounce easily, and handles quick string crossings with ease, and beginners looking for something that is easy for them to get a good tone out of, and that feels good in the hand. At this point, it is very personal, and is like choosing your magic wand.
Some cellos are more picky then others, and finding a good performing, compatible bow can be a challenge, and other cellos pretty much love every bow you try. On average, the cellos we come in contact with reject about 1/2 to 2/3s of the bows that we try on them. Out of a pile of 20 bows that we have tried, 6-10 will make the 'maybe' pile, the others will have been rejected due to incompatibility.
More expensive doesn't necessarily make a bow more compatible. And although we love pernambuco, some cellos actually perform better with a carbon bow. It's a very personal thing between the bow and the cello that is not easily quantifiable.