I have access to hyacinths, mums, and pansies at the moment, though I've seen windflowers pop up in the store as well. I've gotten some hybrids from mystery tours, namely pink and purple mums, and purple, blue, and orange hyacinths. I've planted a lot of colors and types of flowers haphazardly, though I haven't found any roses or lilies yet.
One lily of the valley did sprout today (see above pic.)

More will come, and I realized today because of where I've placed most of my fencing, the majority of them will sprout up on the same plateau I'm planning on moving my house to.

I'm also thinking of trying for a crop of golden roses now that I have the gold watering can.
I've done zero work or coordination with flowers in AC games before, in fact until New Leaf I ignored them entirely, so this is a new AC gameplay system to master.

Possibly the last one...