I started my journey by playing laser tag.
We started with a couple world of wonder lazer tag sets (still have a new in the box set), eventually graduated to an 'electronic survivor shot' setup (my favorite), and tried many others along the way. Photon, Laser Challenge, Sega Lock-On, Laser Challenge Pro, as well as playing at the professional places that kept stats on little keyfobs.
Eventually we got into customizing our guns, by purchasing nerf guns or other gun models (video game console guns for example) and transplanting the electronics from store bought guns into the new cases. The internet was growing every day at this point, and using AOL we were able to scour the internet and found several other people with a similar interest. Eventually we found a few really industrious people who even went so far as to build their own electronics from scratch, and they had even taken the time to give a basic explanation of how the gun worked, and how you could build a basic laser tag gun from scratch with a couple 555 timers. Later we found someone who went the extra ten miles and build their own circuit using a PIC16F84A microcontroller. At this point, my eyes were large and glistening.
So my journey began, and I found along the way this project offered a lot of education in a very small package. Frequency modulation, LED driving, Audio for the sound effects, microprocessors (or timers), assembly or C programming (if using micros), control systems, infrared communication, optics for increasing range/controlling spread... etc etc.
As far as beginner projects went, I picked a doozy!

Eventually, the laser tag craze died down, and most of my collection was relegated to a few totes in the garage. I still have them of course, and I have many custom guns, but its been a long time since I played. With that project a great many other projects suddenly became possible and my passion for electronics was in full bloom.
Eventually I went to college and got my associates in EET. I still have every plan to go for my bachelors, but currently I am still paying off my student loans (over half-way done).