Beautiful. You have the right approach....let the garden show you it's delights and attack its weeds first.
The yellow flower in your first photo is probably an invasiveweed that already has its own "what is this" thread.
There are some serious (expert) gardeners in town. I am a novice - but here's my best guess at identification:
#1 - I think the green shoots are hosta.
#2 - looks like a Japanese Maple
#3 - No clue. It could be honeysuckle, trumpet vine, wisteria - I don't know.
#4 - Daffodils
#5 - looks like hydrangea - I would hold off pruning this shrub, because some varieties bloom on old wood. There are threads on MOL about pruning hydrangeas.
#6 - tulips, of course).
#7 - hyacinth
#8 - forsythia - you can prune this back hard, and it will still live
#9 -assorted bulbs
Your surprise garden looks beautiful!
I'd suggest making a graph/grid of your garden, showing what is coming up where. By autumn, it might be hard to remember where the various bulbs are coming up now, and you'll probably want to add more for next spring's blooming. A grid will also help you know where you will have bare spots all year, and where you have bare spaces in either spring/summer/or fall. Once you know that, you can fill in with perennials or annuals to give you the look you want. And if you want to add a shrub, you'll know what is around and under the spot you'd like to plant it in.
lynnl199 is right, #1 is Lily of the Valley. Yes, they spread and are very difficult to stop -- they'll strangle other stuff. If you're energetic, dig most of it up (with a spade, not a trowel) and dump it in a barrel for the Spring Rakeout boys. But leave some, it really is a great smell.
I agree with most of what sweetsnuggles said. But I don't think #5 is hydrangea, it's too vertical and doesn't branch. But I don't know what it is, maybe Rose of Sharon.
I ran into the same thing when we moved here 25 years ago -- a wonderful experience running into flowers I'd never even seen before. I still have peonies and lilacs and azalea and -- really -- columbine that date from that move.
If you have open spots that you're pretty sure don't have perennials waiting to pop, run over to the Maplewood Pool parking lot on the 7th to get even more stuff at the plant sale. You're going to love your garden.
Promote your business here - Businesses get highlighted throughout the site and you can add a deal.
PS Bonus: a deck and a patio. I'm envisioning a gardeners F2F with everything in bloom....