When it comes to Website/Creative Design strategy, the most important part is knowing the audience and the content that would support your design. Somewhere I had read earlier that -
A Design without Content, is just Decoration
So, to begin off, firstly you will need to know the trends that are prevailing in the particular industry where your design is going to go, the competitors, their design philosophy and thinking, as most of the times the firms hiring you would ask you to beat the other site in design thinking and product presentation. Go through the sites, read the content and best strategy these days is to have a story that can be told of how the product/company can help the viewer of the site.
There was a mastercard web-landing page where they used SVGs to present the use of mastercard in order to make the lives of the people better and more easier.
Once you are fine with a design philosophy and style that you would like to go ahead with, then you can get in touch with the Content Writer person, as the site can only target better if the content is good enough. Best would be if you can use that content in a better way and present them in various forms of images and icons, like ZOMATO uses.
Once the content is finalized, (this is also the state nearly from where the redesign of website starts, as the content there is already finalized once), you can go ahead, take the branding colors into consideration and use them wisely across the site to make a branded feel to the design, try to stick to the colors that you have in the logo itself, with just black and white as the extra colors being used. Try to bring in the style and feel of the logo into the design, FORMAL/CASUAL/FUNKY/GAMING/etc.
This will help in connecting better to the website and the story that you are going to tell. Try to keep the design simple and clean with good tab on typography as that is quite famous these days. Also if you can integrate a good set of Iconography, that would add to the classiness of the overall design.
Try to produce what you would like to see on the webpage/creative design, and stick to that with some minor changes as per the requests. But always be open to feedback that might be jolting, as the client might surely be knowing the customers better at times and can help you out if you take the feedback positively.
And lastly, have fun, play around, and try new things without hesitating, we learn by failing. Be ready to fail. If you don't fail, you have't tried something new at all.