I'm trying to make a world where my "humans" have ZW sex-determination system that means sex is determined in the ovum instead of the sperm.
Could I just easily hand-wave everything else as being the same, beside mother gametes deciding is it going to be a boy or a girl or there would be some crucial differences due to ZW system?
I would like to keep the settings as scientific as possible, and minimize the hand-waving.
Certain genetic diseases would function differently. In real life, men are heterogametic (they have one copy each of two different sex chromosomes, XY), whereas women are homogametic (they have two copies of one chromosome, XX). This gives two vectors for genetic diseases that affect men more strongly than women. Obviously, harmful genes that are on the Y chromosome don't affect women at all, and harmful genes that occur on the X chromosome are less likely to affect women because they are often recessive. In women, a healthy gene on the other chromosome will override the harmful one. In men, there's no second copy to fall back on, so the harmful one is always expressed. This also means women can be carriers of the disease (having the gene, but no symptoms), whereas men must always be either symptomatic, or free of the disease.
With a ZW system, this is exactly reversed: women must be heterogametic ZW (so that they have a copy of each chromosome to pass on to their children) whereas men are homogametic ZZ. Therefore women would have the same vectors for genetic disease that men do in the real world. Likewise there would be genetic conditions known for being latent in men, but expressed in their female relatives.
Family and gender roles will not change. From parent's point of view, gender of the child is still random. Female still can have only a few offspring, so they will care more about them than males will.
The difference in genetic diseases that Cadence mentions is true, but it seems that such diseases are pretty rare to begin with.
The biggest effect will be more genetic variation in female, as wolfie said in a comment above. There will be more female geniuses (but also more freaks). So I suspect women will play a bigger role in science and industry.
I agree that it wouldn't make a drastic impact as far as any phenotypic sex characteristics are concerned (if your species is like humans are: not-particularly sexually dimorphic).
However, an interesting side-note is that the sex-determining gene (in humans it's the SRY-gene) will over time make the chromosome it is typically located on (in humans this is called the Y chromosome) smaller over millions of years of DNA replication because it won't have a duplicate of itself. This means that there are certain traits in other animals that you could potentially capitalize to round out your world-building:
Female calico cats are able to express a mozaic of colors on their fur because they have (I believe the word is) co-dominant genes on their X chromosomes. In your world, this could happen with male cats (or your humans if you wanted them to be less similar to us).
Male Peafowl are able to be more colorful for a very similar reason. The Victorians thought that Female birds were less colorful because they had to hide to protect their children, but there is a reality that they couldn't express as much color because of their chromosome count.
Female birds tend to be larger than their male counterparts. Male mammals tend to be larger than female mammals. This could change your world, should it be factored in. The chromosome with the 'sex-determining gene' tends to be lumped with some advantageous genes regarding, height, muscularity, et cetera because only highly advantageous genes stay on the gradually-decaying sex-determining chromosome (ie. the Y chromosome in humans).
Similar to the feature of color expression in female mammals and male birds, perception can be enhanced/damaged should genes be found on the sex-chromosomes. For example, in humans, the rare people who have 4 different kinds of color cones in their eyes (Red, Green, Yellow, and Blue) all have XX chromosomes and therefore tend to be female. On the flip side, Color blindness is much more common in males than in females, although if a female inherits color blindness from a carrier or afflicted mother and an afflicted father, she can be color blind. In your world this sex-based (dis)advantage would be flipped.
It's fancy stuff.
To conclude, your females would have live birth just fine. Your people could be as similar to us as you wanted, but if you want to have this important genetic feature, you may want to include some quirks in your world-building that would line up with what we already know.
It's all up to you though :) There are exceptions in nature to every trend I listed above.
