Using a variational calculation, we have considered the effect of chain length, intrinsic backbone stiffness, solvent quality, and salt concentration on the behavior of a single semiflexible polyelectrolyte in dilute solution. Explicitly, we have calculated the radius of gyration (R-g) and effective persistence length for different solvent qualities and salt concentrations. For an isolated semiflexible polyelectrolyte with increasing molecular weight, there can be five regimes with effective exponent nu (defining the molecular weight dependence of R-g) being 1, 1/2, 1, 2/5, and 1/2 in the absence of nonelectrostatic excluded volume interaction. This suggests a double crossover behavior from rodlike to Gaussian and then to Gaussian again as the chain length is increased. During the second crossover. nu can be as high as 1, although the actual value of R-g is order of magnitude smaller than the rodlike value. There can be another regime in this second crossover where the apparent exponent is 2/5 due to additional self-screening arising from counterions of the polymer. This self-screening can significantly reduce R-g, although the asymptotic exponent 2/5 may not be observable due to physical constraints. A thorough analysis of the crossover behavior is presented.