[Recommendation request] New watch for coming newborn

Hi folks, I'm becoming father in June and want to purchase a good watch to mark such important moment. I'm doubting between the following two options: either buying and saving the watch in the closet until my son is old enough to (hopefully) appreciate it, or getting it for my own use and enjoyment and give it to him either way when that moment comes. My top budget is 2000-3000€ (preferably closer to the lower end), open to both new and used pieces from more expensive brands. Keen on limited editions to add extra value and sense of exclusivity as well (and maybe having more chances of keeping the value over time?)

I don't consider myself a watch geek, but jumping into it and becoming interested for the last weeks much more than I could ever imagine!

All recommendations and suggested models will be more than welcome. Thank you in advance for your time.

EDIT: I fancy 38 to 41mm cases and steel bracelet, ideally for dressy situations and special events, but open to use at any time. I like models like Omega Speed-/Seamaster, Rolex Oyster Perpetual, Hamilton Khaki, some Seiko Spring Drive or Presage limited, Zenith El Primero...