ROBOTS!
Why send a bunch of under-evolved meatbags to understand a machine, when you can send the most advanced machine available to understand its alien counterpart?
If not, then two distinct teams
1. the one aboard the reconnaissance vessel (you get it for free, given that they find the artifacts)
2. a team of nuclear physicists/engineers, which arrives on a specialized ship equipped with our computers and large-AIs
A bit of reasoning below.
TL;DR sending a lot of humans in space for the just-in-case is way more expensive than sending just-the-necessary-right humans with a good encyclopedia and a powerful computer (we're in the future afterall).
Let's consider a real-life case first: the discovery and study of the Antikythera mechanism. When we look at page listing the team that analyzed and figured out the artifact and its inner workings, one thing becomes evident: the team changed/expanded over time as the understanding improved and goals evolved. These people were of course working from the comfort of planet Earth, and relied heavily on computers and other types of equipment. A lot of the experts were simply there to be asked questions, but did not necessarily need to do any "field" work. Without detracting from their expertise, we can presume that an encyclopedia from the future could have been almost as effective in providing a similar level of contribution.
Back to the case described by the OP, following the OP's timeline, there seem to be increasing understanding of the alien tech and thus changing goals. There are going
1. The first team is already aboard the ship, if the ship was sent to study the celestial body. This is exactly as the OP outlined it. In fact all that they need to do is to identify the rocky formation, measure the radiation and raise a flag for sending someone to continue the research. I imagine we are talking about a chemist (also acting as geologist) and the ship's chief engineer, who is trained in nuclear physics. A geologist is unlikely to be aboard provided that rocks strata are not going to change quickly, and there is no need to dig/build/do anything with them during a reconnaissance mission. This team gets as far as wearing a suit and going on site to record radiation from close to the pillars, perhaps even collecting a sample.
2. Radiation occurs spontaneously, so there must be something unusual about this particular case. Perhaps the next goal may be to understand the source/pattern of the radiation. There goes the nuclear physicists/engineers team. 199
Nuclear physicists and engineers do have enough computer science and math training to discover, identify and study unusual patterns. I imagine that the large AI can be found by looking at some kind of patterns. This team travels on a spaceship of the future, which will be designed to perform detailed analysis. We can safely expect the ship to have the equivalent of future wikipedia stored in its mainframe, as well as future state-of-the-art AI technology to assist in the analyses. This team has all the required knowledge to figure out the presence of a wormhole, the existence of antimatter reactors and engineer a simple interface to interact with them. I am not claiming that they will understand the mechanism, or that they will be able to reverse-engineer them, but that did not seem to be the question in the first instance.
Notes: The following experts have been left on Earth:
* Linguists. If current AI can translate between human languages today, future AI can probably identify some elements of communication between us and aliens.
* Miners. Unless the goal is to extract the pillars, in the OP question there is no need to dig big holes.
* Military, security details. Maybe they come for free as pilots aboard the ship. But considering that the planet/moon is inhabited, as reported by the reconnaissance mission, these people would just be useless cargo load.
* Doctors, biologists. Beyond what's typically aboard future space vessels, there is no need to add any. All research can be done from the safety of spacesuits, or even within the walls of the spaceship, provided drones to go out an explore.
* Mechanical engineers, architects. There was nothing mechanical in the structures identified in the reconnaissance mission. Also, the OP did not specify whether there was the need to build anything, in which case I'd rather send builders. Hence, beyond the chief engineer to look after the engine, there is no need for these expertise.
* Radio/communications experts. to evaluate the signals and attempt contact with the AI.
* Mathematicians, computer experts, theoretical physicists. Theoretical people are not exactly what is needed in the first step of looking at an artifact and figuring out how to interact with it. These are instead the people that may be employed later in reverse-engineering the apparatus.
* AI psychologists, astronomers, archeologists, alienologists and historians. 199