Preface: I'm not a designer or a clotheshorse so these descriptions may be a bit rough
Abaya just means "cloak"; there are many kinds of abaya, just like there are many kinds of jackets/coats.
Just like most other things, the interpretation of the abaya varies differently from one region to the next. For example in the UAE abayas have large flowing sleeves and look more like a giant graduation gown than anything else.
In Bahrain - there are other styles.
Even in Saudi Arabia, styles vary greatly depending on the area you are in. In the Eastern province its a bit more relaxed as you have a large influx of expats (thanks to Saudi Aramco HQ) and a lot of weekenders from Bahrain.
The objective of the abaya is to deter wandering eyes; so therefore it should not be one to attract a lot of attention; and it should not show your features that would attract unwarranted attention from the opposite sex.
That's what it is supposed to be.
However, these days you'll find form-fitting abayas that leave little to the imagination, abayas adorned with Swarovski crystals and logos of their designers; some even with sequins and other embellishments.
I grew up in the Eastern province and much has changed over the years, here are my general tips:
You don't need to wear an abaya, if you are already modestly dressed. This means, no bare shoulders, no tight jeans, no crop tops; it is also recommended to wear full sleeves and loose fitted clothes. However, this is only accepted in major shopping complexes and I would not advise this as general practice. It is always safe to have an abaya handy.
You don't have to cover your head (this is called the hijab); as many non-Muslim women do not do this.
If you do decide to wear the abaya, there are many types you can choose from depending on how your fiance prefers to dress and what makes her comfortable. Remember that the idea is to cover yourself up such that you are not attracting unwanted attention.
There are complete abaya "dresses" you can buy, which is like a full length gown you wear (sometimes on top of your regular clothes); here is an example:
The general form however, looks like a loose fitting coat, like this:
The more modern interpretation is of a more fitted tailored gown, with some individual touches. This is what you will find in the shops and what most young women prefer: