About you asking for "present clothing" character design... All you gotta do is observe modern wear. And you can dress your characters up as you please. The reason why character design classes go more into scifi and fantasy garb is because it is all based off of the entire history of fashion--they also go over functionality of clothing and accessories, because that is important to understand and convey in design (ie why Aragorn wears a shirt that can have its sleeves detached--because he's a ranger, that's all he wears, so if it's hot out he can take his sleeves off or use them for something else easily.)
Personally, as someone who is into fashion, you should really check out fashion history. It would give reason to the today's fashion that you're talking about. "Fashion isn't an island, it's a response." -- incredibly important to remember. I highly suggest a string of short-form lecture videos by Professor Amanda Hallay called Ultimate Fashion History. If you like fashion and want to learn more about it, it's best to start with a fundamental knowledge of attire and its purpose. And she's really great in the videos! She makes it fun. :}
There's also a great book called Adorned in Dreams. It's honestly my favorite thing to read. An excellent analysis on fashion history, sex and gender, and classism.
Another way to go about it, if you're not too keen on fashion as a hobby, I highly suggest to look into the fundamental folds. Then observe clothes you like that are on people--draw them that way with the volumes in mind. Apply your observations for when you are clothing your characters. It really helps to solidify your knowledge, and not just copy aimlessly. So keep that in mind! I hope this is all somewhat helpful.
Here is part 1 of a video series by ModernDayJames on clothing folds. This video really helped me a lot to use for when I observe attire. :}
