Okay this is my experience after living in Jordan for 5 years.
If you are more weary toward ISlam, go for the abaya, for Allah's sake. BUT if you are not that religious, wear what you want because in Amman , I've seen women wear sluttier cloths then women walking down Daytona Beach in 90 degree weather.
So I'd go conservative--long sleaves, ect. don't show your chest, don't over do the make up--just look like you---if you want to go Islamic..do the abaya thing. I have an extreme pet peeve against these women here who where tight tight jeans and like a tight long sleave slinking shirt thinking that it's "Hijab" or Islamic...and it's not, it's disgusting, and most women who dress like that get no respect from people, only fear of the government and police is what keeps men from following them, and even still...they get jeers and harrassment, AS opposed..to the woman wearing tight jeans and a short sleave casual business blouse...people seem to fear here more because she's usually they type who will scream in the middle of the street if a guy even so much as looks at her the wrong way...the hijabi ladies are usually afraid and are many times stocked (especially if they go out at night alone)...
Abaya:::Abaya is good if you are NOT looking for a job. Abaya is a stay at home thing. But if you are looking for a Job in an abaya, good luck, because maybe only .07% employers will hire you here in JOrdan wearing an Abaya. But if it's to impress someone..go for it...you'll be respected more..and just be careful not to be alone with the guy..because really, online dates usually turn out to be really really bad..men usually have on intention in minde, especially jordananians looking for foreign women.
Back home men are bored of the sex scene, here it's extremely hidden but men thrive after it---it's disgusting...
GOD I want to go back home!!!!!!!!!!!