We investigate the ground-state properties of the spin- XXZ model with power-law-decaying () interactions, which describe spins interacting with long-range transverse (XX) ferromagnetic interactions and longitudinal (Z) antiferromagnetic interactions, or hard-core bosons with long-range repulsion and hopping. The long-range nature of the couplings allows us to quantitatively study the spectral, correlation, and entanglement properties of the system by making use of linear spin-wave theory, supplemented with density-matrix renormalization group in one-dimensional systems. Our most important prediction is the existence of three distinct coupling regimes, depending on the decay exponent and number of dimensions : (1) a short-range regime for (where in the gapped Néel antiferromagnetic phase exhibited by the XXZ model, and in the gapless XY ferromagnetic phase), sharing the same properties as those of finite-range interactions (); (2) a long-range regime , sharing the same properties as those of the infinite-range interactions () in the thermodynamic limit; and (3) a most intriguing medium-range regime for , continuously interpolating between the finite-range and the infinite-range behavior. The latter regime is characterized by elementary excitations with a long-wavelength dispersion relation in the gapped phase, and in the gapless phase, exhibiting a continuously varying dynamical exponent . In the gapless phase of the model the exponent is found to control the scaling of fluctuations, the decay of correlations, and a universal subdominant term in the entanglement entropy, leading to a very rich palette of behaviors for ground-state quantum correlations beyond what is known for finite-range interactions.