A summary-like review was written on the females I think Tasuki had the best connection with, even though the chances of a relationship were unsuccessful. All opinions are based on the observations I made from watching/reading the Fushigi Yuugi series and the Genrou-den manga. Spoilers are evident.

Name: Reirei
Age: 14
Siblings: One - Keiron of the Mt. Kaou bandits
Loved by: Keiron; Kouji
Set backs:
1. She was a member of the Mt. Kaou bandits, the group that provided the greatest opposition to the bandits of Mt. leikaku.
2. She died.

How did they meet?
They met when Tasuki and Kouji infiltrated the Mt. Kaou stronghold on a mission to steal Keiron's most valued treasure. Reirei willingly allowed the two bandits to kidnap her once they found out how much she meant to her brother.

Relationship:
Tasuki's dislike for women made him oblivious to Reirei's affections. He eventually grew fond of her as time progressed, but more as a friend an nothing more. She was a sweet young girl and would have done anything for Tasuki (actually she did). And once faced with death, she finally admitted her love for him bringing the red-haired warrior to tears. If she were still alive, there's a possibility that they could have been together.

Name: Miaka
Age: 15
Siblings: One - her brother Keisuke
Loved by: Tamahome; Hotohori; Nuriko; Amiboshi
Set backs:
1. She was the Priestess of Suzaku, a girl from another world.
2. She fell in love with Tamahome.

How did they meet?
Miaka, Hotohori and Nuriko were in search of the fifth Suzaku Seishi. One thing led to another and the group ended up being abducted by Mt. Leikaku bandits. Genrou (Tasuki) then showed up unsuspectingly, and kidnapped Miaka from his fellow bandits. He eventually confessed to her that he was the fifth warrior of Suzaku.

Relationship:
Tasuki's blossoming feelings for Miaka was something that surprised even himself. To him she was different from all other girls, her outgoing personality strongly overpowering him. His will to protect her was truly genuine. It's a bit sad that the first girl he ever fell in love with was deeply in love with someone else.