Well done Bob. For a first time viewer using only info from Nerdsmossis you got the vast majority of things right. Including little details like where some of the characters come from. Particularly impressive was your guess about Strax the big head guy. Yes he is a Sontaran, and old school classic Dr. Who antagonist race. Pretty much Who's equivalent to or satire of Klingons.
I know some have compared Capaldi to Sylvester McCoy, but honestly his look, mannerisms and such remind me a little more of Jon Pertwee, with maybe a dash of Colin Baker thrown in.
If you are going to start trying to make sense of it all then as others have suggested the 2005 re-introduction of the show is the best place to start. The premier episode of that Rose is in a word "fantastic". Chris Ecclesten was one of the shorter of the Doctors runs and they did not quite settle on the tone until halfway through his run, but he still has some astonishingly good episodes in his small pool of 13. I recommend Rose, Dalek and the Empty Child / The Doctor Dances two parter. The two parter is one of the creepiest Who stories that doesn't involve the Weeping Angels and bonus it introduces John Barrowman as Captain Jack Harkness.
Davis Tennant is often viewed as the most common favorite of the modern Doctors. He strikes a good balance between charismatic charm, pure whimsy and dark, oh my can he go dark. Noteworthy stories; The Girl in the Fireplace (which has a connection to this episode you just watched), School Reunion (just for the return of classic companion Sarah Jane Smith and K9, oh and Buffy's Anthony Head), The Runaway Bride (for introducing what later becomes his BEST companion Catherine Tate as Donna), Blink (which is the first Weeping Angels episode so you may have seen it, but still amazing), honestly there are so many good Tennant episodes, but topping the must see list would be the two part Silence in the Library / Forrest of the Dead and The Waters of Mars (for just how dark and utterly powerful the Doctor is. Do not watch this one until you are well familiar with the character.)
For Matt Smith, I know he is very well liked, but honestly I always thought the best part of his run was the various and always amazing supporting cast that flow around him. The Eleventh Hour is the initial must see with him. and honestly if you have made it this far you will probably be watching the full run if Smith just to catch up. Day of the Doctor, 50th anniversary special is noteworthy and a must see, although a little disappointing as it isn't what it could have and should have been.
If you do seek to delve into the Classic Who, I would as much as possible start with Tom Baker the 4th Doctor and go forward from there. Jon Pertwee is fun too, although his stuff feels a little more dated and may be better appreciated after Baker, Davidson and the rest. The William Hartnell and Patrick Troughton stuff is a bit harder to watch. Quality on every level is bad (the shows were not well preserved, many are lost to history), pacing and such is very off comparred to todays standards. They are interesting to watch from a historical perspective, but to play catch up it is almost better to simply read episode summaries at least initially.
I would also strongly recommend the recent BBC TV movie "An Adventure in Space and Time" as a must see introduction. It focuses on the creation of the show and it's leads. The SJW in you will love it as it is mostly about Verity Lambert, one of televisions first groundbreaking female producers.
Welcome to Galifrey. All of Space and Time awaits.