FF1 Origins was a great remake, and I especially liked the high-quality music, though I didn't like the translation style, and the gameplay just didn't feel as smooth, fast and fun as it was in NES or WSC. FF1 DoS is just as great as FF Origins, and while it lacks an FMV (which has hardly anything to do with the storyline anyway) and doesn't have top-quality audio, the game still looks and sounds impressive, and the music quality is high. I also prefer DoS' translation to Origins', and it stays more loyal to the original FF1. "I, Garland, will knock you all down!" FF1 DoS' gameplay is faster, and the system is more user-friendly. If you're a new player, FF1 DoS is quite an easy game so you should be fine with it, though for those looking for a challenge, FF1 Origins has the choice of Easy and Normal difficulty.

If it was for FF2, I'd definitely go with the DoS version. The translation issue is the same as with FF1, I prefer the DoS translation. The same for gameplay, the system in FF2 DoS is a lot more user-friendly and more fun than in PSX. Leveling up spells is absolutely tedious in PSX. If you're new to FFs, FF2 PSX is a very hard game and it doesn't let you select the difficulty. FF2 DoS doesn't let you select it either, but the game seems easier.

To see more comparison between different FF1 & 2 versions, check this thread. Have fun with whichever game you choose to buy.