Neural network to classify data with probability

I've been educating myself on neural networks, and have come to realize the best approach is to "try some" and find a model that works best with the data I have.

I have n measures of a single item. Right now it is just 4 measures, but we will be adding more in the future. It probably won't get too high, so I don't think high dimensional networks like Deep Learning are appropriate.

The tricky part is that I have i sets of n measures which I want to compare to j sets of n measures.

It is actually more nested than that and I've implemented a Nested ANOVA (Hierarchical ANOVA) for analysis. But I am trying to explore using a neural network to identify hidden relationships.

The relationship between my n measures is complex and unknown. I would like to use unsupervised learning to generate probabilities of classification for a single set of n measures. Then, I could I could take those i or j samples and build a histogram for the collection. Now my i x n and j x n samples are the same dimensions.

Again, I could train a new network to classify those collections. Ultimately, I'd like a mechanism to identify which collections of n measures are similar.

My reason for posting is to get some feedback on where to begin researching on how to tackle this. I know it is going to be an experience in learning!