Using the USB to Serial Communication Board

Ok I want to make a project(not important here), but if I use my Aduino UNO clone here in India, the judges and people will think that I'm using some readymade product of some brand with the covers removed, exposing the Circuit. Infact many won't know what Arduino is or even what a Micro-controller is and what it does.So I decided to make my Arduino a stand alone one and read This Tutorialorial - http://arduino.cc/en/Main/Standalone

I don't want it to be able to connect to a computer (once I have burned the programme using my board).So can I omit out the USB to Serial Comm Board?

Also I want to use an LCD but not a 16pin one as it consumes away almost 10 pins.Is there any low pin LCD like one which uses I2C or so.(ok even if it uses 3 or 4 of my Arduino pins).

InduinoX:
I don't want it to be able to connect to a computer (once I have burned the programme using my board).So can I omit out the USB to Serial Comm Board?

You can leave out any pieces you don't need. If you don't need USB I/O you can remove that. If you don't need a manual reset button you can leave that out. If you don't need 16 MHz you can leave out the crystal and capacitors, If you don't need an LED you can leave that out. If you have a regulated DC 5V supply you don't need the voltage regulator and capacitors.

The parts you really need:
The ATmega328P processor.
A 10k pull-up resistor on pin 1 (Reset)
Ground on pins 8 and 22.
Power (4.5-5V) on pins 7 and 20 (VCC and AVCC) (they accidentally show 21 instead of 20)

You can get LCD boards that use I2C, SPI or async serial. These typically only require between 2 and 4 wires (plus power and ground).

Stuff about minimal boards: Gammon Forum : Electronics : Microprocessors : How to make an Arduino-compatible minimal board

I put together another one today BTW:

If you don't need to "talk" to a computer you can omit almost all of the labelled wires.