Arduino and 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,