I would like to learn and begin to program a little sensor, like a temprature sensor, etc.
The "simplest" way to measure temperature is with a thermistor (a resistor that varies with temperature). You put a standard resistor in series and apply a voltage to make a [u]voltage divider[/u]. Then you use a program like the [u]Analog Read Serial Example[/u] to read the analog output. It's a bit tricky converting the readings to temperature because thermistors are not linear, and voltage dividers are not linear either (a voltage divider puts-out a voltage related to the ratio of the "bottom" resistor to the total resistance.) But, there are formulas and algorithms so you don't have to work out the math yourself. ...A thermistor probably isn't the best-final solution, but it's an easy way to get started.
There are also solid state analog-linear temperature sensors such as the LM34 & LM35. Those are just about as easy to use as a thermistor but they are linear so the software is much simpler. (And they are pretty-accurate, even before calibration.)
If you are going to use multiple sensors, there are temperature & humidity sensors with digital I2C interfaces. Eventually that's probably what you'll want to use, but that takes another special library and I'd recommend starting out with something more straight-forward.
I will download Arduino to learn programming.
Of course you'll need the hardware. The software (firmware) runs in the Arduino hardware.
. My programming skill is limited to Net for the time being...
... Hope am not too old to learn (40+y) .
Since you've done some programming you should be OK. Programming in any language uses the same concepts of looping and conditional execution.... Learning your 2nd programming language is easier than your first. The tricky part about the Arduino is that it doesn't come with a display so it can be difficult to "see" what your program is doing and difficult to debug. But, you can helpful little messages to the serial monitor. Or, once you have your LCD connected & working you can use it. (The LCD is not plug-and-play... You have to wire it correctly and write software to make it work.)
You'll also need to learn a bit of electronics if you don't know any.
Are there different LCDs for different program applications (like temp sensor, humidity sensor, moisture sensor, etc)
As hobbyists, we usually have to use general-purpose displays. (High-volume manufacturers can get special displays made.)
There's an LCD library, but you'll have to make sure that your particular LCD uses the same hardware connections and protocol. (Or, modify the connections & software appropriately.)