When reading, I encountered this expression and do not quite understand. My guess is: "She is very gentle (?) like her appearance."
The conversation:
Mc's Big Sister: 「ああ～ 生き返りますそーちゃん、そーちゃん会いたかった～。昨日の夜ぶりだね、会いたかったよぉ～」
二本木家次女、僕の二番目のお姉ちゃんこと二本木日和は見た目通りのおっとり系だ。
I assume your question is mainly about おっとり.
A dictionary definition as follows:
人柄・しぐさなどが、落ち着いていてこせこせとしないさま。おおようなさま。「―（と）構える」「良家の出らしい―した振る舞い」
Taken positively, it means calm, non-hectic, generous, soft. Sometimes it could be used somewhat negatively meaning slow, non-responsive. Opposite characteristics I can think of are eager, aggressive, restless etc.
As for 通り and 系, see the following:
Overall, the phrase means She is a soft-type as her appearance suggests.
