Logo design

For a new small business
I’d like a logo in 2 different shapes - 1 to fit a circular social media icon and the other a cover photo.
I want something simple with elegant (not bold) font. Colour palette pastel pink and burnt orange. The name of the business is Rosebud and Ginger. I’d like Rosebud to be in the burnt orange font fading into pastel pink for the word Ginger.
I’d like the & symbol or the R of Ginger to look like a rose if possible. In any case, I’d like a rose in orporating into the logo.
Id also like to know the specific colours used so can keep this consistent.
The next project will be for the web design, so please let me know in your proposal whether this is something you can do, as I’d like the same person to do both.
I have uploaded a photo of something I did quickly on a free website. I’d like this building on.