Yes, surely you can use any USB cable for charging your smartphone. The cables available today in the market are generally universal, so you can buy any USB and use it. It is such that just to provide the customers with a complete package, the manufacturers of the phone will provide you with these accessories. The only difference could be with the compatibility of OTG, which you need to check out with your phone and the cable that you purchase, nut apart from that, it is only the quality of the cable that matters.
Now going for a renowned brand ensures that you get an unused new one, but in local stores, there is no such guarantee, the shopkeeper may hand over to you an used one, which he has bought second hand, and in that case, you could be at loss.
Next, comes the length issue, it is all the same. Nowadays, to avoid tangles, the manufacturers are making the wires shorter, as the more it gets tangled, the more connectivity and electricity flow gets disrupted. SO, while choosing, it is advisable, not to go for too long ones.
Coming to your next question of "fast charging" and "normal charging", it is required to know that "Quick Charge" is basically a marketing terminology used for showcasing the power management capabilities of the circuitry in a smartphone and its wall charger. That implies that to make the "fast charging" work both the phone and the charger need to have the supporting technology for quick charging. But, that does not mean that you need a Qualcomm processor phone to avail that facility.
A quick charging can be supported in all the end devices that are contingent on the power controller alone and not dependent on a larger chipset. For that matter, Qualcomm has licensed the technology to non-Qualcomm smartphones as well. So, while purchasing an independent USB charger, make sure to check on these issues.
