Can I connect 3 baseboard heaters rated at 120 v and 1500 watts to 1 t-stat to control all of them?
What size wire and breakers do I have to use? And shoud the t-stat be single pole or double pole.

Each 120 volt 1500 watt heater needs it's own separate 15 Amp circuit with #14 -2 plus ground cable and a 15 amp circuit breaker.

Each circuit will needs it's own single pole t'stat.

If you absolutely need to have one t'stat, it gets more complicated that the t'stat needs 120 V control voltage to operate a 3 pole contactor that would then operate the three heaters.

If you have limited experience, apparent by this question, you may need a professional to install a contactor system.