I like seeing the really old art/fanart of the characters and I'm thinking of drawing some of the older designs. I like to see how much has changed since the beginning. Where can I find some of the really really old stuff, like fanart of the beta designs for instance?

Oldest you can get is the original RAITA sketch that spawned Katawa Shoujo. Came from the back of a Nausicaä doujin he made.
https://cripple.booru.org/index.php?page=post&s=view&id=1570
Colored in by fans: https://cripple.booru.org/index.php?page=post&s=view&id=1

You can look through the dev blogs to see how their art of the characters evolved over time.
http://katawashoujo.blogspot.com/2011/11/shizooooon.html
http://katawashoujo.blogspot.com...h-direction-complete.html
http://katawashoujo.blogspot.com...h-direction-complete.html
http://katawashoujo.blogspot.com...h-direction-complete.html
http://katawashoujo.blogspot.com...ase-of-emi-ibarazaki.html

Also just searching through the devs art will get you some of their earlier art pieces. Interesting one for you may be 'Kekekeke' who designed the sprites for the Grid1 demo early on in Katawa Shoujo's development.
https://cripple.booru.org/index.php?page=post&s=list&tags=kekekeke
Sure you can find a rip of the Grid1 sprites somewhere out their too if you want.

As for pure 'fan' fanart, it's hard to say. With the death of the Shimmie a lot of context for art has been lost but you can use the 'Wayback Machine' to see how the Shimmie was. You can also look through the forums to see older fanart. Unfortunately some used now obsolete image hosting sites, but there is still a decent amount to browse.
https://ks.renai.us/

Check out Gamera. A very interesting case in KS history since they made fanart based purely on the RAITA sketches before the threads on 4chan that started the whole project.
http://gammatelier.free.fr/page.php?art=amp_classroom

Hope this is helpful.

Thanks for showing me this!I used to play katawa shoujo when I was a tween actually (yeah, I know, that's way too young, but i turned the sex scenes off lol) and I'm and adult now so I pretty much look at Katawa Shoujo stuff out of nostalgia. I looked at the Shimmie a lot back in the day. (and saw a lot of stuff I didn't want to see.) I feel like if people who didn't much about katawa shoujo knew I liked this game they'd assume weird stuff about me but it's really nostalgic for me and I really got attached to the characters back then. I used to draw Hanako all the time who was younger and it was fun starting another drawing of her recently. Sorry, that's kind of ramble-y of me. I looked through some of the Shimmie on the way back machine but only some of the pictures seemed to be fully saved. At least that's how it seems on my phone.