If all you've played is Ys III, then you're in for a... well, I'm not sure. Chronicles can feel a bit dated, but that's because it uses the classic style of Ys combat - slam into an enemy (at an angle) to kill it. It's fast-paced but it can be a little off-putting. My recommendation is that if these don't do it for you, invest in Oath In Felghana, which is a retool of Ys III using the Ark of Napishtim (Ys VI) engine. Combat is still very fast-paced, but it feels a bit more modern in that you actually have a button to swing your sword, and even some rudimentary combos. It's quite good. My personal favorite is Origin which also uses the Ark engine, but shouldn't be played until after you've gone through Chronicles.
Fun fact, did you know that Ys III was originally going to be an unnumbered gaiden? The original plan was to release it simply as "Wanderers from Ys." Makes sense, especially given that in series chronology it comes after Ys IV.
Edit: As a note, avoid enemies until you reach Minea. You'll get some free money which you should spend on equipment, and that will make killing enemies a _lot_ easier.