By popular demand, here is my post including the main websites I use to collect stats that I use in my podcast. Enjoy!
General stats: https://www.baseball-reference.com/, http://www.thebaseballcube.com/, https://www.mlb.com/stats/. These websites are all great, and hold your baseline stats like ERA and Batting Average, and also have their fare share of advanced stats. Both Baseball-Reference and The Baseball Cube also hold minor league stats. Both Baseball-Reference and The Baseball Cube hold tons of baseball information about teams, players, events, and anything else. For general stat searches, I would start at either of these databases.
Advanced stats: https://www.fangraphs.com/, https://baseballsavant.mlb.com/. Though the General stats sites do indeed have advanced stats, these sites are dedicated to them, with Fangraphs holding more mathematically advanced stats and Baseball Savant holding more tangible Statcast stats in the form of interesting charts and graphics.
Rosters and depth charts: https://www.fangraphs.com/roster-resource/opening-day-tracker . This website is likely my favorite one. It clearly displays every teams projected rosters, projected minor league rosters, top prospects etc. It works as an all-in-one place to get all information on a team that you need. I use this resource the most for division and team breakdowns.
Minor league stats, prospect stats, and scouting reports: https://www.mlb.com/prospects, https://www.baseballprospectus.com/prospects/, https://prospects365.com/, https://www.prospects1500.com/. As you know, the minor leagues are my favorite part of baseball, and I follow prospects and minor league teams to the same extent that I do Major League ball. For individual prospect stats, I recommend searching them on The Baseball Cube (mentioned and linked above), but you can also find tons of minor league data on these sites. MLB's prospects page gives detailed reports on every teams top 30 prospects, incoming draft prospects, and international prospects. Though to find news, Baseball Prospectus and Prospects 365 do the trick. My favorite in depth scouting site is without a doubt Prospects 1500, as each teams writer posts a detailed pre-season and mid season top 50 prospects list.
In regards to apps, I recommend downloading the MLB At Bat app as well as the MiLB First Pitch app for respective information. Both these apps need work, but are the best available at this point.
I hope this breakdown helps. If I missed or forgot anything, or you have any other questions, feel free to contact the podcast here.