We perform global hybrid (kinetic ions and fluid electrons) simulations of the solar wind coupling with magnetic dipoles of different strength and study foreshock morphology and its influence on the bow shock and magnetosheath. The advantage of the hybrid code over fluid codes is that it treats ion-scale microphysics in the context of the global interaction. We study the characteristics of the ultralow-frequency (ULF) waves generated by kinetic instabilities and find two types of waves: (1) sinusoidal almost parallel propagating waves and (2) highly compressive obliquely propagating fluctuations. In contrast to suggestions made in the past, we show that compressive waves found near the shock do not evolve from the sinusoidal wave population but rather are generated by a different ion population. We find that the sinusoidal waves are generated by field-aligned backstreaming ions, while the compressive waves near the shock are generated by gyrating ion beams closer to the shock. Our results show that, for low dipole magnetization, noncompressive waves dominate the foreshock, while compressive waves grow just in a very small region and do not have time to evolve, so no quasi-parallel shock is formed. In contrast, when the system scale size is much larger than an ion inertial length, highly compressive waves convect into the quasi-parallel region, evolving into large steepened structures that eventually form the shock transition. These waves play an active role in shock dissipation processes and eventually form part of the wave spectra in the magnetosheath. Comparison of our results with observations shows that the characteristics of sinusoidal waves in our simulations resemble the properties of 30-s sinusoidal quasi-monochromatic waves in the Earth's foreshock, while compressive waves have similar properties to the observed right-handed steepened fluctuations. Downstream from the shock, the magnetosheath is permeated by a variety of waves that result from the convection of upstream waves and also from local generation. The wave characteristics are different in the quasi-parallel and quasi-perpendicular parts of the magnetosheath.