>>723695768 (OP)
If you're not a faggot who cries like a bitch from older games not having a camera controlled with the right stick then go for DMC1. The best way would be to emulate the original PS2 version as the HD Remaster is fucked visually.
Then you can move to DMC3. In this case the best version depends on what experience you'd like to have. PS2 Special Edition is good enough all things considered, the first PC port is fucked up beyond repairs and even with all the fan fixes it may crash randomly. HD Collection on any platform is fine, I guess, and you can give it more tweaks and quality of life improvements (that may break difficulty balance) using DMC3 Crimson mod.
Then DMC4. Special Edition if you want to replay as some other characters and/or use newer consoles. With PC it depends on whether you want to launch the game on a potato or not, as the OG DMC4 on PC has a god-tier optimization.
And then DMC5 for good measure. Special Edition is console-only, btw. Also, you can try DmShit and DMC2 afterwards if you're curious enough.