I had random assortments of old computers and peripherals I would tinker with for years before I ever knew what a mechanical keyboard was. I imagine some of those old boards may have been mechanical, but I have no idea. Those, along with the computers they were meant for were usually free.
The first I know of is my first Corsair K70, with MX reds. I think it was on sale for $100 or so within about a year of that model's initial release. It still resides on my desk, although it doesn't see much typing lately outside of gaming when I have 2-3 random other rotation keyboards plugged in at any given time.
First one ever - no idea, it was too long ago, I didn't take any specific notice of the keyboard, and they were generally supplied as standard back then.
First one I remember - NEC APC-H4100E that I got with an NEC APC 4 PowerMate 4C '286 computer (no, the NEC APC-H4100E that I have now is not the same one).
First modern mechanical keyboard - Ducky Shine 1, red LEDs, Cherry MX blue switches - $172.
Hard to beat NEC blue ovals for a first mechanical switch.