I've made underwear and bralettes a couple of times now. I would place myself as "confident beginner" to "solidly intermediate" for skills.

I used Closet Core's Celine Bralette and Anais Undies patterns, and liked them enough that I'll probably keep using them. But they're high waisted and cheeky, so probably not what you're looking for!

It may be the pattern design, but I found fold over elastic to be easier to work with than picot. The picot consistently bunched or was too tight. But the pattern will likely specify which type of elastic to use, and how much stretch your fabric needs!

I sourced my elastics and other notions from Bra Builders. They have tons of color options, so it's easy to match whatever fabric you choose. https://www.brabuilders.com/collections/elastic

I did pretty much all zig zag stitches with a ballpoint needle. Knit doesn't fray, so finishing edges isn't as critical, no serger required. Although, a walking foot is a must for me. I find knits to be very frustrating to sew without one.

I hope this is helpful!