Plus-Disc & Kagetsu Tohya ☴
After reading Tsukihime, I recommend reading Plus-Disc and Kagetsu Tohya in that order. Plus-Disc is about two hours long and acts as a gateway into Kagetsu Tohya in a way. You will most certainly need a guide for Kagetsu Tohya, as stated by Bingus in "Why should I read Tsukihime?" it is definitely an... early... concept. It's a great read either way. Don't be intimidated by the flowchart, you don't need it unless you need something extremely specific but the guide should cover everything.
Melty Blood and it's Manga ☴
Melty Blood is one of the most iconic and influential anime fighting games out there. It has gone through many versions leading up to what we have now, MBTL, but if you want to check out the story you just need to read Melty Blood Re-act, Act Cadenza, and then Actress Again Current Code. You can find a download for every game here. You don't need to play the original because Re-act acts as a remaster for it, greatly improving the jank combat and various other things. Melty Blood also has a manga series which I highly recommend once you're done playing the games. The art is wonderful and there's even one dedicated to Kohaku shenanigans (Melty Blood Act-2). The proper reading order is simple: Melty Blood >> Melty Blood Act-2 >> Melty Blood X. As for TYPE LUMINA, that is Remake material.
Melty has a very active community with plenty of information on all the characters. There is a Discord where you can post art or play games with other people and a Wiki with all the character info you'd ever need. You can also check meltyblood.club if you're just starting out and want to get into it since it has everything bundled together. Lastly, there is also an inactive forum, Melty Bread, but everyone uses the Discord since it's just where everybody is nowadays. Even though that's the case, there's still info available on the forum and can usually help with weird niche stuff you might be having trouble with.
*For online play, there is a caster with rollback netcode you can easily get in the #important-links-info channel of the Discord. Nobody uses the Steam version to play online but you can support the developers by buying it.
All Around TYPE-MOON, TAKE-MOON and Carnival Phantasm ☴
Before Carnival Phantasm, TAKE-MOON and All Around TYPEMOON screenshots reigned supreme. Both of these manga throw TYPE-MOON characters into funny skits and exaggerate their personalities quite a bit. Carnival Phantasm needs no introduction, this iconic anime has been the grace of early TYPE-MOON fans and beautifully animates the characters everyone knows and loves. While it does leave some nice scenes out, you can always read the TAKE-MOON manga to see what they left out. You'd be really surprised with what they didn't include.
Shingetsutan Tsukihime Anime and Manga ☴
I know it sounds ridiculous, but watching the Tsukihime anime that many say doesn't exist is worth it as a group watch with some friends. It's a wonderful example on how not to adapt a visual novel. This 12 episode anime somehow has a filler episode and there's been a rumor floating around since the dawn of it's existence that the director didn't even read Tsukihime. It even has a Portuguese dub!
As for the Manga, it is an entirely different level of quality. The art is wonderful and the story is consistent, some would even say it's a good alternative to reading Arcueid's route but it still has some things from outside of her route.