I had to retype this entire comment as my browser froze near the end of it , anyhow here we go again.

every time I see the “not quite Saber” girl it catches my eye

That's gonna be Arcueid (the non-neco neco-arc), she's the poster girl of the VN. Her design is similar to Saber in more ways than one and it is even more ~~horrible ~~obvious in the remake.

If the UX is approximately as good as Fate then it would be no problem, although it seems like it’s not voice acted

OG Tsuki does not have good UX, ONScripter is downright primitive compared to Kirikiri and has next to no real styling options. Another thing to note is that Tsukihime was originally made right off the heels of Kara no Kyoukai with little budget. Tsukihime pretty much built Type Moon as a company to the point that the name "Type Moon" itself is a reference to Tsukihime. That said all of this is something you'll quickly get used to and by the time I made it to the second hook (~2h in) I was too captivated by the story to really care about this aspect of the VN.

That said, if the UX and lack of voice acting make it really unplayable you can start with the remake (although you will have to jump through some hoops in order to read it in english) and it does alter things quite a bit. Another thing of note is that the remake is going to be 2 games with the current game only being the first 2 routes (referred to as the "near side" routes) and no date for the second game has been given as of yet. I'd definitely say to give the original game a proper try and see from there.

In any case, it’s always fun to see a dedicated fan of a single series

I'm not just dedicated to Tsukihime, there's a good few other series I really like; but I haven't done too much in regards to those here yet, another aspect is that it is a really good VN that besides the manga doesn't have any adaption the community almost memed out of existence (if you thought the DEEN Stay Night adaptation was considered bad you're in for a ride). What I really like about Tsukihime though is that it doesn't spend it's time explaining every detail of the world and magic system (there is some exposition; but nowhere near what Fate has) and expects you to pick up on these details yourself.

PS: depending on how you interpret the question above Tsukihime may not be the oldest VN as that would go to Mahoutsukai no Yoru even though it's never been properly released until it's VN remake in 2012.