Can an old pentium III processor still be useful?
It would be very difficult to use.
It's a processor and not a microcontroller, thus you will have to provide everything :


external ram (is the ram controller inside on PIII? ) DDR are not that easy to implement.
Power supplies. I am sure it needs several voltages and you will have to follow a precise power up sequence.
Chipset? how do you interface something with the high speed bus of the PIII? There is no connections for FLASH, IOs, USB or something. Theses are generally done by the chipset. You could replace it by a high speed FPGA, but you need to have access to the PIII datasheet and bus specification to know how to interface with it.


etc...

It is feasible, but it's very complex. 

In a personal scale from the easiest to the hardest :


HERE, EASIEST PROJECT EVER
Do something with an Arduino
Do something with a Raspberry Pi
Design your own circuit and PCB (not a clone of something found on the web)
Use a recent (not PIC16F84) microcontroller without libraries. Just bear metal programming using only the MCU datasheet and a good compiler
Do some tricky analog design
Do some simple FPGA design (including the board)
Design a processor platform from scratch (a new kind of raspberry pi)
Design into the RF world
Do advanced FPGA design
Try to use PC world busses from the low level (PCI PCIe BT USB2.0 ...)
Design a PC
MOST DIFFICULT


Trying to do a kind of chipset to interface with a high speed bus of a PIII belongs to the end of my previous list.