Hi lilcrowgirl and welcome!

I have been able to grow herbs on my NE-facing balcony, mainly because it does get sun in summer (but not in winter). If your balcony is up high enough and/or away from alot of trees, you may be okay (I'm in a hi-rise above all the trees).

Since alot of folks grow those types of herbs indoors and they do okay, you might be fine with them outside as long as you stick them in a spot that is the brightest. The plants might be a little leggier than usual, but you might be surprised how they turn out. Often potted plants do quite well with morning sun/afternoon shade as all-day full blazing sun can fry them and watering becomes a several-times-a-day chore. As an example, cilantro is one that prefers cooler, moist, and non-blazing conditions, where basil can take it drier (but not too dry or it will droop).

Regarding container size - it depends on how much you want to grow for harvest. I direct seeded basil into 8" and 10" pots and that was plenty for me to make pesto (I still have some left). If you buy plants of the herbs, you could pot a couple into a larger container (maybe 12") and let them fill out that container during the regular season.

Potting mixes are often a personal choice item (some people make their own and others will buy a mix). If you buy, don't cheap out - get a decent "soiless container mix".

The other thing is that some of your chosen herbs are annuals (basil, cilantro) and some are tender perennials (rosemary, lavender). The latter two will probably need to be brought in for winter if you want to save them for next year.

Parsley! Does wonderfully in shade. Mint does well too. I also *do* grow basil, thyme, and marjoram in 3/4 shade, and get enough to use. However, they grow much more slowly than usual, so plant more than you need.

If your balcony is shady, you might do better buying plants than starting from seed.