I did a simple digital thermometer as my first 89C51 (Intel's 8051 architecture based - www.8052.com) microcontroller
It used:
1. LM35 temperature sensor (linear output) - VERY easy to use
2. ADC0804 for digital input to uC
3. LCD display.
So, you basically get a lot of practice doing just this simple project. It's better to do it in Assembly. You would need to learn only 10-12 instructions.
The best book for this is "THE 8051 MICROCONTROLLER - mazidi & mazidi"
PICs are quite cheap, you can choose from 8 bit to 32 bit mcus.
The IDE and assembler can be freely downloaded from the microchip site. The assembler uses just 35 instructions, you can also buy a C compiler at a later stage.
Also there are thousands of PIC based projects that you can choose from in the internet.