Congrats!
The only thing you need to be REALLY careful of is wiping her bottom so you don't give her a UTI. Always wipe front to back. Teach her to do the same when she's old enough.
Other than that, it totally depends on the personality of the child, just like it would for a boy. I will say that girls' clothes are a lot cuter and come in a much larger range of colors. Boys' clothes come in: primary colors.
As for your specific questions:
Tights: I only put them on in the winter when it gets cold. You can also do leggings under a dress if you like.
Diaper covers: Usually come with the dress you're buying. As they get older, if you care about modesty, you can add bike shorts or something similar under the dress. I didn't, but dd started to get teased last year by the neighbor kids, and so she started adding shorts on her own at age 6.
Heels: Not on my child until she can buy them with her own money. (OK, we've got one pair of dress up shoes she wears, but they're only for dress up.) I don't wear heels, so it's just not an issue. They're bad for your feet/legs.
Pierced ears: This is very cultural. I don't come from a culture where pierced ears on young children are the norm, so my daughter won't have her ears pierced until she can take care of them herself.
Where to buy clothing: I look more for fiber content than anything. Dd has incredibly sensitive skin, so we don't mostly 100% cotton. We like Hanna Andersson, but they're really expensive. So, I look for them on Ebay and in thrift shops. Dd is developing her own sense of style. Friday she wore to school: Black leggings with red/white hearts, a blue dress and a purple sweater, topped by a mermaid necklace. None of it matched, but it filled her needs.
Otherwise, any good children's clothing maker should be fine. I like; OshKosh, Carters, Gymboree, Children's Place, Baby Gap, Old Navy. I buy leggings at Target because of the price and because they don't have to be all cotton for dd.
Gender roles: Expose your dd to a range of them. Give her a range of toys to play with. Trucks as well as dolls. Expose her to both t-ball and gymnastics. Science as well as art. Then let her choose. My dd tends to choose rather traditional 'girl' stuff - she'd rather swim and do gymnastics than t-ball. Our neighbor's girl chooses 'boy' stuff -- soccer, baseball, etc.