Selective single beam tweezers open tremendous perspectives in microfluidics and microbiology for the micromanipulation, assembly, and mechanical properties testing of microparticles, cells, and microorganisms. In optics, single beam optical tweezers rely on tightly focused laser beams, generating a three-dimensional (3D) trap at the focal point. In acoustics, 3D traps have so-far only been reported experimentally with specific wavefields called acoustical vortices. Indeed, many types of particles are expelled (not attracted to) the center of a focused beam. Yet the trapping capabilities of focused beams have so far only been partially explored. In this paper, we numerically explore with an angular spectrum code the trapping capabilities of focused beams on a wide range of parameters (size over wavelength ratio and type of particles). We demonstrate that (i) 3D trapping of particles, droplets, and microorganisms more compressible than the surrounding fluid is possible in and beyond the Rayleigh regime [e.g., polydimethylsiloxane (PDMS), olive oil, benzene, and lipid sphere] and that (ii) 2D trapping (without an axial trap) of particles with positive contrast factor can be achieved by using the particles resonances. The 3D trapping of biocompatible functionalized PDMS particles with integrable, high-frequency focused-beam tweezers opens the way towards acoustic force spectroscopy in some force ranges that were not accessible with optical methods.