Being born in the 70s, by the time I realized I was a person, Integrated Circuits were already all around us - although our TV was still mixed technology (vaccuum tube and solid state), which was the only piece of electronics we actually used as kids.
Starting the hobby in the 1980s, my dad had already a wide variety of parts including CD4000, SN7400 and the regular linear parts (555, 741, 386, etc.) - I still have most of them inherited from my dad.
I don't recall what was the exactly first thing I assembled using an IC, but something I really loved and vividly recall were the typical counters: 555, 7490, 9368 or 7447 (depending if anode/cathode), etc. Also the CMOS variant using 555/4510/4511.
Later I moved on to audio mixers (741) and amplifiers (TBA820, LM380, TDA2012) but, without much knowledge about noise, ground loops, gain, etc. it was an exercise in frustration - the hum/noise/distortion sources were very mysterious to me.