I guess I can safely assume they are all weeds, except this one which I believe to be Virginia Creeper? Can I kill them with round-up or do I have to pull their roots? There are tons and tons of them.

You can always use roundup.

The garlic mustard you have to pull and bag as floral said so that the seeds aren’t dropped. Do this ASAP since the seed pods look well developed and IME they will start dropping seed relatively soon. The seeds have the potential to remain viable for years, so you will want to learn to recognize them so you can pull them as soon as you see them. If they don’t yet have flowers or seeds, you can use glyphosate, and mulch will reduce the number new plants you get.

Thanks all. All of them have been pulled. Should I spray the soil with something to prevent future weed seeds before planting shade garden plants?

There are preemergent herbicides, but they can interfere with certain plants’ growth, so instead I would mulch well. Many weeds require light for seeds to .germinate. Then just plan to spend a bit of time each week pulling any weeds you see when they are small so that things stay under control.

Garlic mustard is an ongoing battle. Plan to spray it with roundup in the fall a couple weeks after first or second front, after most everything else has gone dormant. Also a good time to spray japanese honeysuckle and ground ivy (glechoma hederacea).