Get strings from Serial.read()
You're adding the ASCII value of each char to your string, hence you get numbers. See the various String constructors at:
https://www.arduino.cc/en/Tutorial/StringConstructors

Either cast the read byte to a char:

stringOne = String(stringOne + String((char)incomingByte));


or consider receiving characters as chars, instead of ints:

char incomingByte; 


There is a perfectly valid one-method call which does all of this hassle easier and more efficiently: https://www.arduino.cc/en/Serial/ReadStringUntil

Note that you'll sooner or later anyhow have to add a framing prototcol. For example, you're sending down text commands to Arduino, and each command is separated by a new line character. ReadStringUntil will handle that very nicely.