I'd stay away from the LCD for a little while if this is your very first project. Just because it probably requires a microcontroller to control the LCD.
The 3 LEDs is a bit difficult to do. 2 would be simpler. Because in electronics it is easy to tell if something is above or below, but it is very difficult to tell if something IS something else. Usually it ends up being if it's below "desired value+a little bit" and above "desired value - a little bit" then you can consider it that value. But you already have those two and are treating them as different LEDs.
Making 2 LEDs would need 2 comparators- one for each LED to say if it is above or below. To make the third one to tell if it is "around 21 degrees" you would need 2 more comparators to say if it is within a certain margin of 21 degrees. You would also need an AND gate to combine the output from both comparators (you can use an op-amp as a slower comparator if you just wire it up like a comparator with no feedback).
A thermistor isn't even a voltage so you use it as one resistor in a resistive divider. Thermistors are very high resistance which means they are not good at driving loads (ie. it is like a battery with a very high internal resistance...it burns off a lot of the energy it tries to output inside itself). So you would probably need to buffer it with an op-amp and amplify it, or do whatever signal conditioning you wanted to do with it. But you only need one thermistor (thermistors of the same kind are never exactly the same anyways so if you multiples for the same thing you might get 2 slightly different temperature readings at once)
My suggestion is to use a row of LEDs (different colours if you want...blue for the cold end, red for the hot end). Have each LED be driven by a comparator, and each comparator has a different reference voltage. WHenever the temperature (respresented by the voltage output from the op-amp ) gets above a certain value, light up the LED. THat way you get a bar graph for temperature that gets shorter or longer as it gets colder or warmer. It's simple, and it looks nice.
How much do you know so far anyways? It was a bit of a pain to write the above post because I wasn't sure if you understood things like source impedance (the battery with high resistance example, and high resistance sources being bad at driving loads example) and comparators, op-amps, how they are similar and how they are alike.
Also, do you understand what a thermistor is? It is a resistor that changes value with temperature like a variable resistor controlled by temperature. The difference between a PTC and NTC? PTCs increase resistance with temperature, NTCs decrease resistance with temperature. They aren't made exactly the same way and don't behave as complete opposites so they are better for different applications (ie. temperature sensing, shutting down something when it gets too hot, slowing down the current spike when something first turns on but then allowing more current to flow after it is on) But it is non-linear (double the temperature and you will get a change in resistance that is different. Linear ones do exist, but they are called RTDs and are more expensive, but really REALLY accurate (in fact all temperature standards are referenced to Platinum RTDs- the most stable, linear, and accurate of all).
And if you do, then I suppose you understand how you can use a thermistor as the lower resistor in a resistive divider to convert the resistance into a voltage? The thermistor's resistance changes, but the top resistor of the divider stays the same, which means the ratio of the divider changes changing the voltage output of the divider. You can measure this change in voltage and calculate backwards to figure out the resistance and thus temperature.
Last note, like I mentioned, thermistors are non-linear. So it's easiest just to use preset thresholds since you look at a graph beforehand to get the resistance at a temperature and build your circuit to match. If you start having too high resolution (like a 7 segment display) then you need to somehow build that entire graph into your circuit (usually in software and a microcontroller) rather than just 10 thresholds you picked from the graph beforehand.
THis is all really simple stuff...it's just wordy and I have no pictures.