I just realized the first game isn't even on GOG, but I own the second one. Will I miss much in terms of story if I play Soul Reaver first? It sounds like Blood Omen may never happen anyway...

Blood Omen:
You play as Kain. He is assassinated in the beginning of the game. He then makes a deal to seek vengeance even after death. There are many interesting moments in the first installment, which would be rude to spoil.

The answer to your question:
No, you will not miss anything.
Raziel (protagonist) makes his first appearance in Soul Reaver. Nothing much is known about him. He isn't mentioned in the first installment.

"May seem as a Spoiler"
Soul Reaver ends with a cliffhanger. Hinting that everything will be told in Soul Reaver 2.
Legacy of Kain universe, jumps from the past to the future & vice-versa . Different events, in different places, & time.
It's a big jigsaw puzzle. With pieces scattered all over the place.

gogwitcher300

Full Story of Blood Omen (If the game will be lost forever)
https://www.youtube.com/watch?v=5kDzqScUs-E

If you don't plan on playing it then you should look up (youtube) full gameplay or a story so far video. It sets up who Kain is and how we got where we are at the beginning of Soul Reaver. Not required, but it completes the lore.

I would play it, but is there a way to play it on PC right now?

Sup. You will miss a lot of info if you'll pass BO1 and BO2 before playing Soul Reaver, but there is a way to skip all gameplay without missing some important info - just visit one or two fan-sites and read chronology. I know it's difficult to normally start BO1 on PC these days, so it's better to do it this way. :)

So there are TWO games before Soul Reaver?? I'll have some catching up to do!

No, only Blood Omen - the first one. BO2 takes place in an alternative timeline caused by the events of other games. So, you could play it as the last one, after Soul Reaver 2 (the release order), or even skip it entirely - since it differs quite a lot both in the terms of story and quality. I've played it after SR2 and it was fine.

As for BO1, I would try to get it somehow, since to me it's my favourite in the series. It sets the tone for Nosgoth and helps you understand Kain's motivation.

Here is a guide how to run Blood Omen on modern systems (it's quite old, but should still work):
http://www.thelostworlds.net/HowTo/Running_Blood_Omen_on_Windows_XP_and_Vista.html

Apart from awesome dialogs and young Kain's wittiness, there aren't many references from BO1.