So what happened with the refrigerator?
Your question is too broad to cover completely in a forum like this. You need to first get the appropriate hardware before asking about web servers. You said you have sensors and a development board. What's the purpose of the development board? What kind of signals do you have? Analog like voltages and currents, or do you have to talk to devices over a communication bus, like serial, I2C, or SPI to get the readings? If you're dealing with voltages and currents then you will need some kind of DAQ device. What kind depends on a LOT of factors, such as the actual signals, and your specific needs (e.g., software vs hardware-based timing, triggering, form-factor, cost, interfaces, etc). I would strongly recommend that you contact the local NI sales rep to discuss this.