Are the particles found first and retrofitted into the Standard Model?
Or does the model act as a map of sorts by telling us where to look? If latter, does that mean we're not looking for particles outside of the standard model?
So the SM is a map telling you where to look, but a very sneaky kind of map. In the sector where the strong force matters, it's as if someone encrypted a map, and for every new destination you want to find out about, you have to expend computational resources to decrypt it. In principle, you have all the information, but in practice it is hard to extract predictions from the theory. That is a very peculiar situation for scientists to be in: to have a definite, precise theory, and the opportunity to do experiments, but to struggle to compare the two!
Anyway, these particles are predicted by the SM, where "predicted by" means after expending a lot of computation to understand the strong dynamics one finds out that these particles (which are quarks held together by gluons) should be there.
The approach seems to be we observe a lot of behaviour, then build up models to explain that behaviour. If particles need to be made up to balance an equation then they get made up.
You project that model into some scenario to say "If this model is right, the following ... will happen" and observe. If you're right then work goes on for further evaluate "What about this scenario" and finally a big machine gets built to directly work out, from all that's prior, if a particle that needs X,Y,Z properties really does exist is should be seen in the measurements that are supposed create it.
So to answer your question; Both?
E.g You could take the model, put it in a computer. Simulate what the LHC does and look at that graph of kind of particles it makes. Then you build the LHC, actually smash some things together. Same graph?