Yeah me too in 1982, using the Melbourne House Z80 reference, aged a young 10 years old. Working with POKE and no macro-assembler, I wrote mnemonics then translated them to machine-code by hand. A baptism of fire that to this day that I've not forgotten.
I have my ZX-81 (with the 16KB expansion pack) and my ZX-Spectrum (with a microdrive). I think they're in working condition though they haven't been powered up like in 30+ years.
Don't just plug it in! The power supply and/or VRM can fail in ways that deliver bad voltages to components. You might want to watch some of Lee's[1] videos first on how to bring up a ZX81 safely, or ask in his discord community for more help.
Watching the retrocomputing enthusiasts, apart from obvious things like water damage, it seems that the first thing that one always has to check before attempting to power up is capacitors. A generalism true for all old electronics, rather than Sinclair-specific.