Hello anon !!( ´ ∀ ` )ノ
Thank you so much for writing to me !! I love answering questions :3,, for the sites I go to when looking for older anime media, it truly depends !! I usually look for a lot of imagery of older moe-art styles/older 2000's rooms that fit the overall 'animecore' vibe (* ^ ω ^)
I use the internet archive for nearly everything. Not specifically for finding things already on the archive,, but for finding lots of other hotlinks to older jp websites and blogs mainstream google searches don't usually gather ^u^,, the awesome thing about these personal (and sometimes company) jp blogs from the 2000's, is that nearly all of them have tons of other sites linked that relate to the website or are kinda in the same niche as the site. So for example, if I click on a site from Internet archive, I can usually find a page filled with directories to other sites which eventually leads me down a rabbit hole of sites that probably haven't been accessed in years.
Sometimes for the internet archive, I have to sift, as in-- sometimes webpages that are newer are shutdown/won't load, so I'll have to go back to an earlier date to be able to access it's contents. Sometimes you'll find different graphics based on the year you click for the site as most of them constantly updated :3,,
Other places I look that aren't as common would be google lens! Strange, I know,, but usually if I have a niche image or character, I just put it into google lens and it kinda leads me to more niche old forums with the character or even the origins of the image itself, which usually leads me down a rabbit hole as well (b ᵔ▽ᵔ)b
As for search terms,, I've definitely had more luck with japanese names typed into the search bar vs regular english translations. If you need an accurate translation to something, I usually use MFC (myfigurecollection) and I go from there. I also try and focus on older VN names, UKGK's, and anything that could possibly fit in with the theme I go for on my blog :3,,
I recommend shying away from broad search terms such as "old 2000's anime" or "animecore" since most of the images you'll find aren't exactly 'archivable' since they're still very easy to access/already floating around on the internet in mass. If you just wanna post cute images, then those terms are great !! But if you're specifically trying to archive, you'd wanna get a little more specific so you don't post an already popular image :3
Overall,, there's no proper way to really go about archiving !! Do what makes you happy and archive what you wanna see and hold onto. I post tons of images that I think people would enjoy but at the end of the day, I personally just enjoy the moe aesthetic myself which is why I upload to this blog ^u^
Thank you so much for the kind words,, it made my night :D,, I hope this helps a little bit !! ヾ(*'▽'*)