I am not familiar with the literature on theoretical/ontological simplicity, so this post might be rehashing material that is well-worn among people who focus on such issues.
I think we can distinguish between two different ways in which a preference for simplicity can be manifested in philosophical inquiry. The first is in the role of adjudicating competing explanations. We have before us a set of rival theories, in competition as explanations of something or other, and we want to generate a ranking of theories from worst to best (presumably so that we may proceed to infer the best explanation). A ranking is going to be generated by scoring the theories in terms of some theoretical virtues (as in, the virtues possessed by theories). Caring about simplicity or parsimony can be manifested by making these rankings sensitive to the relative simplicity of the competing theories. As a first thought about this, it seems to me like simplicity isn't just going to be less important than, say, the virtue of capturing the data but that we will want a method of ranking that produces a lexical ordering where, for any two theories T1 and T2, if T1 is substantially better at capturing the data than T2, T1 outranks T2 regardless of their relative degrees of parsimony/simplicity. At the same time, as I said, I don't know the literature on this and it might be that something like noise in the data would weigh against such lexical orderings in favor of simply placing a lot more weight on data-capture than on simplicity. It is clear that there are a bunch of ways to actually institute the preference for simplicity as playing a role in ranking competing theories, and we can think about those as different versions of the view that simplicity matters in our evaluations of proposed explanations.
Contrast that way of valuing simplicity with a role it can play in guiding theory construction. We have some area of inquiry, like theory of mind, and maybe a general program or explanatory project we are keen to pursue, and we employ simplicity as a guide in our pursuit of the project. Here, caring about simplicity or parsimony can be manifested as a methodological commitment to be conservative with respect to the postulation of new primitive resources. As an example from the early modern period, philosophers offering reductive theories of mind (often in terms of a set of mental faculties/behaviors and a set of mental contents, like ideas) exhibited a wide range of different approaches to theory construction. Some were pretty liberal in introducing new primitive mental faculties or behaviors, while others tried to analyze all of our mental activities in terms of a quite small set of privileged faculties or behaviors.
It seems like the main advantages of adopting this sort of methodological preference for simplicity are: a) that, by severely constraining one's range of options for analyzing things, it consequently provides the theorist with increased direction for proposing analyses (roughly: there is a smaller search space of proposals using only the sparse resources), and b) that, by having fewer resources, it is easier to exhaust them, and thus, our investigations are likely to give us information about what the bare minimum of resources are for addressing a given issue (roughly: fewer resources means, in principle, less you can explain, and so you are more likely to find your explanatory needs outstripping your explanatory resources).
Incidentally, this is a big part of how I understand Hume's project in Book I of the Treatise. Hume's empiricism leads him to adopt hefty constraints on the nature and variety of ideas available on his theory, and Hume further limits himself by proposing only one fundamental type of cognitive activity (which can alternately be labeled conception if we are talking about the typing of cognitive states, or being present to the mind/understanding (with some or other degree of "force"/"vivacity") if we are speaking of the underlying analysis in terms of impressions and ideas. In the case of interpreting Hume, the (a) advantage outlined above produces a nice secondary benefit: it sufficiently narrows the range of viable interpretations of Hume's position on particular issues to inspire confidence about making progress on a number of interpretive debates.
Turning back to things not-directly-related-to-my-dissertation: It seems as though there are important differences between these two ways of implementing a preference for simplicity.
First, the former way assumes we have the array of competing theories already laid out in front of us, and we already know that we are selecting among adequate theories. On the other hand, the latter approach is recommended by, among other things, the high potential for generating inadequate theories. The attempt to rank theories looks like it should be supported by considerations having to do with a propensity for the simplest adequate theory to be true (or for simplicity of an adequate theory evidence of its truth), while the constraint on theory construction is supported by the utility of finding out the explanatory limits of a given set of resources.
Second, when using simplicity in ranking theories, it is important to note that just because T1 is the simplest adequate theory to explain P, and T2 is the simplest adequate theory to explain Q, it does not follow that T1&T2 is the simplest adequate theory to explain P&Q. It may be that T8 was pretty complex among the adequate explanations of P, and T12 was pretty complex among the adequate explanations of Q, but T12 and T8 overlap in such a way that T12&T8 is the simplest explanation of P&Q. So, the ranking of competing explanations of P (in isolation) may wind up being highly misleading about which theory of P we should prefer (all things considered). On the other hand, if T1 is not complex enough to account for P, it is also not complex enough to account for P&Q.
I am inclined to think the latter approach is safer in some sense, since it never delivers recommendations against the true view. I'll probably check out the SEP article on simplicity when I get a chance, but if you have particular recommendations for things worth reading on these topics, let me know.