Particles don't do anything in QFT. It's a field theory and the entity with dynamic behavior is a field. When you think about the interaction point you have to think about a field. The Feynman diagrams that you have seen are a graphical representation of perturbation series expansions for the field, they are not real physical processes. Indeed, not all physical scenarios can even be treated directly perturbatively. Sometimes one has to use non-peturbative method to calculate results for which the perturbation series does not converge (or for which it would converge poorly).
It's only for the space outside of the interaction point where the particle representation makes physical sense. Here the quantum state of the field changes so little that one can replace it with propagating classical particles. The reason for that is because we don't care about resolving the behavior of the field at the level of precision at which momentum and position are non-commuting variables. Instead we are only doing very weak measurements on it. Just like in optics where wave theory gives way to a ray representation when we don't care to resolve diffraction effects, we can substitute particles for the actual excitations of the quantum field far from the interaction point. It's a physical simplification that makes no difference to the results we can measure with our very crude detectors.
This is why you have multiple kinds of simulation codes in high energy physics. There are the codes that calculate what the standard model (and its hypothetical extensions!) has (have) to say about what is supposed to happen at the interaction point (generators), and then there are codes that propagate semi-classical particles trough free space (including electromagnetic fields) and the material geometry of the detectors (transport codes). When you set up a complete simulation of an experiment, you need both. Pythia is a generator, I believe, while Geant would be a transport code. It's been around for a while, I don't know if it has been replaced with something else yet. As you can see, I am somewhat of a fossil.
When you are only interested in the physics of the interaction, you only need a generator. When you are mainly interested in the physical behavior of the detector, then you need mostly the transport codes. Those who do trigger and DAQ simulations usually want a simplified statistical model that's the result of both etc.. It really depends on your application and how much CPU time you can burn.
For your work as an undergraduate you should ask your advisor about the exact methodology that is expected for your work. There are, of course, multiple ways to attack any problem, but I am pretty sure your advisor has a rather specific procedure in mind. Don't waste your time trying to guess what that is. Ask right away what you need to understand and do to make it happen. As a general piece of advice, and you probably know this, already, science is an apprenticeship. The best apprentice is the one who can learn from his master all that the master knows in the shortest amount of time before he/she sets off to surpass the master in the craft. Good luck!