The envelopes and disks around embedded low-mass young stellar objects (YSOs) are investigated through millimeter-continuum and HCO+ line emission. Nine sources, selected on the basis of their HCO+ 3-2 emission from an IRAS flux- and color-limited sample of 24 objects, are observed in lambda = 3.4 and 2.7 mm continuum emission with the Owens Valley Millimeter Array and in the HCO+ and H13CO+ 4-3, 3-2, and 1-0 transitions at the James Clerk Maxwell and IRAM 30 m telescopes. All nine sources are detected at 3.4 and 2.7 mm in the interferometer beam, with total fluxes between 4 and 200 mJy. The visibilities can be fit with an unresolved (<3 arscec) point source and, in about half of the sources, with an extended envelope. The point sources, presumably thermal dust emission from circumstellar disks, typically contribute 30%-75% of the continuum flux observed at 1.1 mm in a 19 arcsec; beam, assuming a spectral slope of 2.5. The fact that at least two-thirds of our sources show point-source emission indicates that circumstellar disks are established early in the embedded phase. The remainder of the 1.1 mm single-dish flux is attributed to an extended envelope, with a mass of 0.001-0.26 M(sun); within a 19 arcsec beam. In HCO+, the J = 1-0 line is seen to trace the surrounding cloud, while the emission from J = 3-2 and 4-3 is concentrated toward the sources. All sources look marginally resolved in these lines, indicative of a power-law brightness distribution. A beam-averaged HCO+ abundance of (1.2 +/- 0.4) x 10^-8 with respect to H2 is derived. The 1.1 mm continuum fluxes and HCO+ line intensities of the envelopes correlate well and are modeled with the simple inside-out collapse model of Shu (1977) and with power-law density distributions of slopes p = 1-3. All models provide satisfactory fits to the observations, indicating that HCO+ is an excellent tracer of the envelopes. Of the 15 sources of the original sample that were either undetected in HCO+ 3-2 or too weak to be selected, seven show 1.1 mm single-dish fluxes comparable to our objects. It is proposed that all of the 1.1 mm flux of the former sources should be attributed to compact circumstellar disks. The relative evolutionary phase of a YSO, defined as the current ratio of stellar mass over envelope mass, is traced by the quantity Integral Tmb dV (HCO+3-2)/Lbol. Sources that are undetected in HCO+ are found to have significantly lower values in this tracer than do the objects of our subsample, indicating that the former objects are more evolved. The sources that are weak in HCO+ 3-2 are indistinguishable from our subsample in this tracer and have intrinsically low masses. It is concluded that HCO+, especially in its 3-2 and 4-3 transitions, is a sensitive tracer of the early embedded phase of star formation.