We present a deep LBT/LBC U-band imaging survey (9 deg2) covering the NOAO Bootes field. A total of 14,485 Lyman Break Galaxies (LBGs) at z~3 are selected, which are used to measure the rest-frame UV luminosity function (LF). The large sample size and survey area reduce the LF uncertainties due to Poisson statistics and cosmic variance by >3 compared to previous studies. At the bright end, the LF shows excess power compared to the best-fit Schechter function, which can be attributed to the contribution of $z\sim3$ quasars. We compute the rest-frame near-infrared LF and stellar mass function (SMF) of z~3 LBGs based on the R-band and IRAC [4.5 micro m]-band flux relation. We investigate the evolution of the UV LFs and SMFs between z~7 and z~3, which supports a rising star formation history in the LBGs. We study the spatial correlation function of two bright LBG samples and estimate their average host halo mass. We find a tight relation between the host halo mass and the galaxy star formation rate (SFR),which follows the trend predicted by the baryonic accretion rate onto the halo, suggesting that the star formation in LBGs is fueled by baryonic accretion through the cosmic web. By comparing the SFRs with the total baryonic accretion rates, we find that cosmic star formation efficiency is about 5%-20% and it does not evolve significantly with redshift, halo mass, or galaxy luminosity.