My primary reference is baseball-reference.com, a source so extensive that I won't even begin to attempt to describe the wealth of data available--I pay the $36/year to subscribe to the Play Index feature, an extremely powerful feature that gives illuminating data and saves untold hours of data compilation. I also use FanGraphs but in either case, I amalgamate data, meaning I combine and augment sources. I do as little manually as possible, but mistakes will occur from time to time, and I claim full responsibility for them. Generally speaking, they should be minor and not affect my conclusions (for example, if I assert that 457 of 503 runners scored from 2nd base on a single, and the true numbers are 455 of 502, is the conclusion that the vast majority of runners on 2nd will score on a single any less valid? This is the magnitude of error I'll make).
On the occasions when I discuss the NFL or the NBA, I use pro-football-reference.com and basketball-reference.com, respectively. It is important to note that both these sites have Play Index features that are FREE to use and can answer many questions (try it yourself--see how many NFL players had 1000 yards rushing and receiving in the same season). There are other outstanding sites, but for any number of reasons (price, ease of use, data presentation, whatever), I find myself going back to these three sites. I also use mlb.com and nfl.com, but not often.
Since baseball is my primary focus, I must state I AM NOT a sabermetrician, nor do I aspire to be one or remotely claim the competence necessary. I admire the work of those that developed concepts such as WAR (something I'll write on separately, since it will be important and a common theme in my writing), but I don't have the facility to create those stats. I work with ordinary box score data, add things not commonly seen (how many base runners were on base when a given batter was at bat? How many of them did he drive in? How many of them did he drive in while making an out?). Again, I don't have opinions, or at least I don't share them--I merely delve through the data and present it.
As a pretty poor debater in my high school and college years, sourcing my material is vitally important to me. To the extent I express an opinion or a thought that is not my own, I will attribute it. In addition, I usually get my inspiration for topics to research while listening to WSCR in Chicago or reading something. Since I'm not the most original thinker out there, I'll always attribute the source of my research ideas if merited.