1) Is there somewhere that has a good "mechanical watches for dummies" type intro/FAQ?
Check out
Teddy Baldasarre. He has a good mix vidoes going over beginner stuff and watch reviews in your price group.
2) Any thoughts on what order/items to buy? I realize I need to provide some more detail here.
In addition to whats already been mentioned, at this price point take a look at Tudor, Baltic and Christopher Ward.
3) What do people tend to like for sizing?
This is a hard one because alot of it comes down to what you like, but you probably cant go wrong with a 40mm. That said, the stated diameter can be misleading because there are many other factors that will also alter how the watch actually sits on your wrist beyond case diameter.
-Lug width, increased length and shallow curvature sit bigger.
-Lug absence/integrated bracelet sit smaller.
-Case shape. Squares & rectanges sit bigger, curved & circle sit smaller.
-Bracelet style. Slim & tapered sit smaller, fat & wide sit bigger.
-Bezel presence, width, edging, and overhang.
Best thing to do is physically go into a store and try it on.
4) Are there features/specifications that anyone thinks are must-have?
BIG NO! Just get what you like because everything has trade offs.
More complications are fun and intriguing, but drains your power reserve, clutters up the dial, has high servicing costs, and often leads to too many pushers & complicated settings methods.
Quartz is most accurate and convenient but boring and quite noisy tick. Hand wind mechanicals are alot thinner but are annoying to always have to wind. Automatic mechanicals are more convenient (just make sure the power reserve is at least >24 hours) and have that visual intrigue of a moving rotor but are generally alot thicker case and require more service intervals.
Gold is shiny, but dents/scratches very easily, is noticably more expensive & heavier, plus the bracelet links will stretch over time. Stainless steel is cheapest but nothing special. Titanium is light but dusky and more expensive. Ceramic is lightest & has that cool factor, but can fail catastrophically without repair options, and are neccessarily bigger. Bronze looks cool and unique, but will patina into something different than what you originaly bought.
Crystals made of hesalite & plastic have a nostalgic vintage look which is desirable to some, but will scratch very easily and visually distorts the dial. Sapphire is most expensive but most scratch resistant. Mineral glass is cheaper but less scratch resistant than sapphire.
If you asked me what traits I would value most in your situation: Sapphire crystal, stainless steel, mechnical automatic with >48 hours power reserve, and if you "like machines" - get an open case back!