While the logo should fit the current web site design it should also survive that we change it.
The web site theme goes in green which can be included in the logo but not required.
Our business is a web shop selling paint at affordable prices online. One of our selling points is that you save money buying the products online and for many orders shipping will be free of charge.
What we don't like about our existing logo is that it is too bland. Our company name is in Swedish and consists of the two words "Färg" meaning paint and "torget" meaning market place. make sure that the second letter in the name "Färgtorget" is an 'ä' (Swedish letter) and not an 'a'.
The web shop is not business to business - we sell to consumers.
The logo type should be a "Pictoral mark". A "Word mark" and/or "Web 2.0" is nice to have but not a must.