Am I not 'right' for a sorority?

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So I've spent about 2 hours reading through a couple of the threads on here, the ones with 10+ plus pages, looking for advice. I found it all very helpful! So, from what I've seen countless times I'll try asking this without giving out too much info.

I am a senior in hs and I do have my heart set on one particular university. Huge greek scene there and very, very competitive from what I've gathered on this site haha. It also happens to be in the south.

I realize many girls grow up dreaming of being in a sorority, or they come from a family that has a history of sororities.
Well, I come from a family where only...a couple of people (literally like 2) have attended college, me being the 3rd. Out of the 2, 1 was in a sorority.

I would love to join a sorority and to find the perfect house for me. Whether I go to the school I hope to or not, I am a tad bit interested in about 2 sororities, because I really like their philanthropies.

Anyways, I guess what I'm trying to ask is...because I would not be going into recruitment with my heart set on a particular house or this lifelong dream of being in a sorority, am I not a 'fit' for a sorority?

I understand being in a sorority is a commitment and something you have to want to do and I do(when I get to college), but since the school I have my heart set on is supposedly competitive when it comes to recruitment, I guess it's maybe killing my confidence and optimism in a way.

Really, I'd be going into recruitment with an open mind and heart, not thinking "I want to be in xyz." But since so many girls go into it with that mindset...I don't know.

I would say what school but I don't want to risk being identified.

Basically I'm questioning whether I'm not right for a sorority because I wouldn't enter into rush with my heart set on any particular house.

Advice?