I would recommend a Nano 3. They are very similar to an Uno, but are able to plug into a breadboard. This will make prototyping all those components easier. With an Uno you will always have a mass of delicate, untidy wires connecting it to the breadboard.
For your lcd, I would suggest buying one with an i2c interface board already fitted. This will use fewer pins on the Arduino.
Yes, if you add enough extra components you will eventually run out of pins. This is true whatever type of Arduino you choose. If you choose a Mega or Due, you can add many more. But even with Uno or Nano, there are ways to add many more components by making best use of the pins the Arduino has. For example components that connect via a "bus" such as the I2C or SPI busses, or even a simple bus of your own design.
The only catch I see here is that the bluetooth uses serial, but there's only one UART on the Atmega 328 - so for boards using that, it would either use the same serial that you're using to program it (might be awkward, depending on what you're doing with it), or use SoftwareSerial (which has some limitations).
If neither of those options is acceptable, you'd need a board (like the Mega) that has 2 UARTs.
Also, you'll need a driver for the motors, either something like an L293D (reversible) or a transistor, relay, or mosfet for single direction drive.
You should be good on pins - Bluetooth uses 2, DHT uses 1, the gas sensors look like they use 2 (1 for each of the 2 sensors), the BH1750 uses 2 (I2C), driving the motors requires 2-4 (depending on whether you want it reversible). 9 to 11 pins used; you've got plenty of pins.
Ideally, you should try to pick up an LCD with the I2C backpack - this is very common on those 16x2 character LCDs - then, it could share the I2C bus with the BH1750 and not use any extra pins.