Hi Kim,
Try googling Marsh Marigold for the first picture. Not sure on your second picture. I have seen this before, but the name escapes me.

I know, I know!
The second one is a great low growing plant called Veronica peduncularis 'Georgia Blue'.
Though actually now I google that name I have found this page from a great perennial site which has the correct identification as Veronica umbrosa. Mostly it is known as Veronica 'Georgia Blue'. I have it and it's one of my new favourites. Nice foliage and beautiful flowers. Good as a low ground cover which spreads.
Welcome to the gardening addiction!
Regards
Susie

Here is a link that might be useful: Veronica umbrosa

Thanks so much Flora... A user on another thread suggested Veronica penduncularis "Georgia Blue" for pic 2. Too bad it's kinda pricy. I was hoping to buy some more to fill in some bare spots!

Hi Kim... from another Kim who resides in an Ohio Zone 6. :)

You don't need to buy any more of that veronica. As the previous poster mentioned, it spreads as a groundcover and so you can probably take out small divisions of it if you'd like to add more of it to bare spots. That said, if you just moved in keep in mind that those "bare spots" may just be places where late-sprouting perennials will turn up. You may want to live there a while and see exactly what does come up before you move or fill in anything!

First plant is lesser celandine, Ranunculus ficaria, a rather freely seeding spring ephemeral that many consider a weed. The second is indeed Veronica umbrosa 'Georgia Blue'. Not sure why it should be all that pricey - it's a very common groundcover here.

The first plant is considered a weed? Really? It looks so, so pretty next to my vinca minor. The vinca minor is separated by a little rock path, but the blue flowers next to the yellow is really so cheerful and pretty.

Purpledaisy, you must have been posting simultaneously to me yesterday :)

Gardengal: maybe Georgia Blue isn't really that pricey. All the websites I visited suggested a price of around $100 for a pack of 24 plants. Maybe that's the going rate, but it sounds pricey to me at least. As a newbie gardener though, I still haven't gotten a grasp of the cost of plants.

Kim