Oath in Felghana and Origin are two of my favorite RPGs ever, so I would start with one of those, preferably Origin first since it is of course an origin story.
Origin is much better after Ys I & II if you can still handle playing those, it's one of those prequels meant to be seen after later events. If you can't stomach Ys I & II then sure, jump into Origin, and it's not as if Ys I & II have some deep rich story anyway (Trails in the Sky comes far closer to being that) so it's no big deal either way.
EDIT: As for which version of Ys I & II to get: assuming you're posting on a PC (age basically doesn't matter at this point) and portability isn't a top priority then get it on Steam.
Runs much smoother and with a wider viewing area if you don't mind a 4:3 picture, and if you do there's a toggle to make it like the PSP version in that regard.