Phantasy Star

Most people may be familiar with Phantasy Star Online, but it was originally a quadrology for Segas 8 and 16 bit home consoles.

The first game in the series was really progressive, but might have been missed by most gamers due to the fact that it was released on the Sega Master System, rather than the dominating console of the time; the Nintendo Entertainment System. Ironically many of the technical feats of the game was intentionally made because it was not possible to accomplish on the NES, but on the SMS.

It was also one of the first jrpgs, the very first having been released the year before: Dragon Quest (1986), later released under the title Dragon Warrior (1989) in the US.

Phantasy Star was released 1987 in Japan and 1988 in the US and UK, but only the Japanese release used the Yamaha YM2413 FM sound-chip (Since the Sega Mark III was only released in Japan), which improved the sound.
Here is a comparison, the Japanese sound from the left speaker, the American from the right speaker.

The main protagonist is a female who set out to avenge the death of her brother.
Even today this is rare, the common trope in video games is for the main protagonist to be a male avenging the death of a female family member.
Back then it was rare to have a female main protagonist at all of course, the only other games I even know of is Metroid (1986 NES) and The Great Gaina Sisters (1987 C64), the second one being a shameless rip-off on Super Mario Bros. (1985 NES).

The team behind the game made a lot of choices to be intentionally different, that is why the game is set in space, rather than a medieval fantasy setting, which was (and still is?) most common for the genre. Although the game was originally planned to take place at 4 different planets, space restrictions only made it possible to have 3 planets in the game.

The battles are much like you would expect from a jrpg, but you could actually talk to some enemies! Also some of the battle backgrounds where animated.

The over-world and towns are viewed top-down, but the dungeons are in first person, which was a first in jrpgs, but not in rpgs all together, although it probably was the best looking first person dungeons of the time.
This was a time before auto-mapping, which means you would have to draw the maps of the dungeons yourself. This is a part of rpg gaming that is lost nowadays, although it did add to the experience of exploration. It's a shame the rest of the games in the series switched to top-down dungeons.

Since it's such a rare gem, you are looking to pay about €230 for a used copy of the game, if you already own a copy, but for some reason can't play it, you can always download a rom and use an emulator to play.