using an ESP8266 through a serial connection with another microcontroller creates a new bottle-neck.
I recommend buying a ESP32 nodemcu
advantages:
- cheaper than an arduino ($6 to $10)
- can execute almost every code that an Arduino can execute and even more
this means the Arduino Uno becomes obsolete the ESP32 does it all
DHT11, and pulsesensor and WiFi all at the same time ithout the bottleneck of a serial connection
because everything is done internally - much more flash (ESP32 4 MB compared to Arduino Uno 0,032MB)
- much more RAM (ESP32 320kB Arduino Uno 2kB)
- faster (ESP32 120 MHz 32 bit Arduino Uno 16 MHz 8 bit)
- WLAN onboard
- more interrupt-capable IO-pins
best regards Stefan