Sorry for the long post, I'm a nerd about this shyt
Right now for Dreamcast I OD'd and spent 200 dollars on a internal mod that allows a hdmi cable to be plugged directly into the the system as if it was a xbox one or something current. A homie I got to know who goes to one of the universities in the city got a side hustle going modding consoles and he did mine
That little slot on the left side under the vent is the newly installed mini hdmi input and any mini hdmi cable you buy out of walmart or amazon will work...the quality is amazing but like I said its hella OD for being a whore for quality. If you don't care about the best of the best and just want convenience you can jus get a 30 dollar HD retrovision cable off amazon
HD Cable for Dreamcast - Hyperkin
Again, this is straight up for convenience and ease...it will not be the best picture quality but still better than ugly ass composite and S-video and makes it compatible with current HDTVs. If you trying to save on money I would personally recommend dishing out 20-30 more dollars and getting a Kuro from beharbros
https://www.beharbros.com/kuro
Beharbros are quality and where I got all my dreamcast cables before getting the mod
PS2 gets a lil bit more tricky. There are ps2 hdmi options available, even by hyperkin who i linked the dreamcast hdmi adapter. The problem is that imo they are all trash and it ain't all there fault. The PS2 has awful output and wasn't properly future proofed at all like the gamecube and xbox was. 80% of the ps2 library is all 480i and it looks atrocious, the only exception are the few games that came with progressive scan 480p support where you would push Triangle and X when starting a game to enable it. But the list is small, like only 20 something games small. So my recommendation is if you can do it, hook up your ps2 using component cables, and not generic ones but official sony ones. PS2 cables are expensive as hell but luckily ps3 component cables are supported and can be found anywhere online so get those. That's what I'm using when I play ps2 and post videos
The best option is currently being worked on, the creator of the DCHDMI is working on a ps2 hdmi mod that will internally impact the whole console and its probably needed the most out any retro system to date. Because the mod will get the picture digitally from the source it will be able to bypass the ps2's 480i limitations completely and output crisp clean 1080p