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The construction of initial data for black-hole binaries usually involves thechoice of free parameters that define the spins of the black holes andessentially the eccentricity of the orbit. Such parameters must be chosencarefully to yield initial data with the desired physical properties. In thispaper, we examine these choices in detail for the quasiequilibrium methodcoupled to apparent-horizon/quasiequilibrium boundary conditions. First, wecompare two independent criteria for choosing the orbital frequency, the"Komar-mass condition" and the "effective-potential method," and find excellentagreement. Second, we implement quasi-local measures of the spin of theindividual holes, calibrate these with corotating binaries, and revisit theconstruction of non-spinning black hole binaries. Higher-order effects, beyondthose considered in earlier work, turn out to be important. Without those,supposedly non-spinning black holes have appreciable quasi-local spin;furthermore, the Komar-mass condition and effective potential method agree onlywhen these higher-order effects are taken into account. We compute a newsequence of quasi-circular orbits for non-spinning black-hole binaries, anddetermine the innermost stable circular orbit of this sequence.Comment: 24 pages, 17 figures, accepted for publication in Physical Review D,  revtex4; Fixed error in computing proper separation and updated figures and  tables accordingly, added reference to Sec. IV.A, fixed minor error in Sec.  IV.B, added new data to Tables IV and V, fixed 1 reference, fixed error in  Eq. (A7b), included minor changes from PRD editin

Circular orbits and spin in black-hole initial data