I'm interested in doing Street Photography, so I'm looking for something portable and I wonder if there is any relevant difference in lightweight between the two lenses.
This really is a matter of preference. On occasion, I go hiking with a Pentax 645N. Back in the day shooters used things like a Graflex. So, whether or not something is "portable" enough is not something anyone can decide for you.
Regarding the lens differences, the 17mm is 120g while the zoom (if I looked up the right one) is 91g. A difference of 29g is about 1 ounce, or a single slice of bread. If this is the straw that breaks your back...well, take something out of your pack and worry less about this.
I also like to do black and white pictures and I sometimes need to zoom and cut them later, so I'm looking for a solution which lets me preserve sharpness as much as possible.
"Doing black and white" and "zoom and cut" (also known as 'cropping') have nothing to do with one-another. All digital images will turn to junk if you crop in and interpolate back up at some point. The only thing you can really do is crop in and not interpolate but limit yourself to the resolution you now have. In today's high resolution sensors, this is usually plenty enough, but you need to worry about the lens being able to resolve that fine detail. This will vary with each camera, lens, and camera+lens combo.
Again - this is something to not worry about. If you are cropping too much into your shots to where they're falling apart, then you need to buy a longer lens. Period.
Another requirement is being able to focus quickly, for I capture mobile subjects: I wonder whether or not the choice of the lenses makes any difference in that.
There's an old street shooter saying, "f/8 and be there." Shooters would set the lens to some pre-conceived distance, the camera to f/8, and the Depth of Field would take care of the rest. Sometimes the hyperfocal distance was used. This allows you to simply point and shoot and get a shot.
Even with fast autofocus systems, this is still a very valid method. Why am I pointing this out? Simply to show you that focusing quickly is as much an operator skill as a camera feature.
Lastly, is there any relevant difference in their market value?
Of course there is. The prime seems to be about ~$150 more than the zoom. Why does this matter? Market value doesn't affect images taken. One of the most used lenses in the world is the Canon 50mm f/1.8 - and it's $125 brand new.
Which is the best option between the two lenses?
Simple really: the one you choose.
Your questions indicate that you are very new to this game. I can understand the pressure of a first lens and to be honest, there are many pro's and con's to either of these choices.
You'll split the photographic community in two on a choice between a zoom and a prime and you'll hear both opinions. The best thing you could do is try them out yourself. Renting the camera and both lenses is the best option so that you can go shooting with both, see and feel the differences, and then make the best choice for you.