GPS is touchy and a pain to get to work well in high dynamic environments like a rocket flight. Here's a link to learn more about programming your UBLOX NEO over serial:
https://playground.arduino.cc/UBlox/GPS
It took me quite a bit of testing to get it working correctly, but I now get high-quality GPS data throughout the entire flight. With only the default settings, you will lose lock immediately and will probably get it back sometime after apogee, about a minute or so. If you want my code, look for it here:
https://github.com/SparkyVT/HPR-Rocket-Flight-Computer
As for timestamps, you absolutely do not need GPS to calculate the descent rate, if that's all you need. Using the clocks onboard the chip is the easiest way. The clock starts immediately when power is applied, and you can access the time using the micros() command. Just get the clock timestamp at each barometric sample and compute the math between. No need to go through the pain of programming a GPS.