We present an investigation of a large sample of confirmed (N=233) and candidate (N=54) Galactic classical Be stars (mean V magnitude range of 6.4-12.6mag), with the main aim of characterizing their photometric variability. Our sample stars were preselected among early-type variables using light-curve morphology criteria. Spectroscopic information was gleaned from the literature, and archival and newly acquired spectra. Photometric variability was analysed using archival ASAS-3 time-series data. To enable a comparison of results, we have largely adopted the methodology of Labadie-Bartz et al. (2017AJ....153..252L, Cat. J/AJ/153/252), who carried out a similar investigation based on KELT data. Complex photometric variations were established in most stars: outbursts on different time-scales (in 73+/-5 per cent of stars), long-term variations (36+/-6 per cent), periodic variations on intermediate time-scales (1+/-1 per cent), and short-term periodic variations (6+/-3 per cent). 24+/-6 per cent of the outbursting stars exhibit (semi)periodic outbursts. We close the apparent void of rare outbursters reported by Labadie-Bartz et al. (2017AJ....153..252L, Cat. J/AJ/153/252) and show that Be stars with infrequent outbursts are not rare. While we do not find a significant difference in the percentage of stars showing outbursts among early-type, mid-type, and late-type Be stars, we show that early-type Be stars exhibit much more frequent outbursts. We have measured rising and falling times for well-covered and well-defined outbursts. Nearly all outburst events are characterized by falling times that exceed the rising times. No differences were found between early-, mid-, and late-type stars; a single non-linear function adequately describes the ratio of falling time to rising time across all spectral subtypes, with the ratio being larger for short events.