25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $\gamma =1.2373\mathrm{}\left(2\right),$ $\nu =0.63012\mathrm{}\left(16\right),$ $\alpha =0.1096\mathrm{}\left(5\right),$ $\eta =0.036\mathrm{}39\left(15\right),$ $\beta =0.326\mathrm{}53\left(10\right),$ and $\delta =4.78\mathrm{}93\left(8\right).$ Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $\Delta =0.52\mathrm{}\left(3\right)\mathrm{}$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.