This isn't a GIS question so much but I'd like to correlate the percentage of the population of census output areas who are children with mean distances to green spaces, but am unsure whether to use Spearman's Rank or the Pearson's Correlation Coefficient. I understand that Spearman's rank is best used for ordinal variables, which I don't think either of these 2 are, so perhaps it's better to use Pearson's? But then I've also read that Pearson's is better used when the relationship between variables is linear which I'm not sure it is in this case, so I'm unsure which option's better. Any advice would be much appreciated.

why not categorize your variables into classes, the use a chi-square test of difference/association between the two variables. This would allow you to see whether areas with high percentages of children live in areas where the walk distance to green space is low. You aren't implying causality in this type of response, since I am sure that is not what is intended.