What are some recommended visualisations to represent how attributes in a data-set influence each other?
Using seaborn in python, I usually plot the pairwise distributions with sns.pairplot. seaborn provides a wide variety of data exploration tools in a high level API, it is quite powerful for data exploration.

Here's what sns.pairplot looks like on the popular iris dataset:


Sometimes plots like the following (a specific kind of cobweb plot) can be useful too.


Those represent the distribution of each parameter on each vertical line, with a web of links joining values for a single entry in the dataset.