Advice/Recommendation needed; Arduino, LCD and UDP over WiFi

Hi there,
being an Arduino newbie and running into my personal Waterloo by "blind"-ordering an Arduino Uno Wifi just to find out that this little stupid is not capable of doing "normal" UDP/TCP, I try to be smarter this time:
What is the recommended Arduino hardware for an application with Touch-LCD (I got a 2.8 TFT Touch shield that seems to do the job) that gets configured and sends events via UDP as a client via WiFi? Or should I better switch to a different platform?

Thanks in advance,
Karsten

What gave you the impression that your esp8266 can't handle "normal" TCP/UDP?

Hi SurferTim,
thanks for your response. I have the impression from different postings here on the forum:

Mid 2016:

March 2017 (!):

It should be possible by programming the ESP8266, but it seems not yet to be available as a library. I want to avoid to dig into ESP8266 programming if possible ;).

Regards,
Karsten