If your goal is to get some understanding of the Clay Problem, you can't really go wrong with first reading the official problem statement and then reading the papers referred to in the document.
On the other hand, if your goal is not the quantum problem but more the classical problem, for the geometers and algebraists a good starting point is of course Donaldson's Geometry of four-manifolds which contains a lot of classical results in the direction (and you can use the reference list to find the original papers should you wish). Donaldson's more recent survey can also be a point of departure.
Since you mentioned that there are participants interested in curvature and Ricci flows, you can also consider discussing the results related to the Yang-Mills heat flow. The standard references are
If you also want to discuss the hyperbolic initial value problem, then a good (classical) place to start would be
There has been a lot of development/improvement/extensions since then (see the References link in mathscinet) but they tend to get very technical very fast (into the details of PDE theory for wave equations) and may be less interesting for your stated audience.