Up until recently, the only way of proving personalisation on web using MC was Predictive Intelligence (Einstein Recommendations). This was not ideal, as this was focused on showing articles or products based on online behaviour, and was very little rule based.
Interaction Studio is able to orchestrate and serve content on all owned channels, and is much more suited to what you are looking for, as it can a.o. make decisions based directly on customer data, without involving predictive engines.
The product has been launched recently (earlier this year) and I have not yet have any hands on experience. However it is a better match with your use case than any of the other features of SFMC
For smaller setups, 3rd party solutions such as https://www.monoloop.com might be interesting. I know Monoloop has built a connector to SFMC, enabling them to use data from there to drive personalisation within their engine on any website. I am not familiar with other products with this functionality, but there might be others offering same set of features.