As we are poised to start our FC game I have been pouring over the FC books and here on the forums/DB to grok the system and my chosen race to play; the ever-humble drake.

Now, let me put a big ol'caveat here: I am
so not proficient in this game yet. We have done a few little one-shot kind of things to horse around with, but no real meaty gaming to get my sea-legs under me on the feel and progression of it all. If questions I ask are redonkulously noob/pedestrian that'll be why. Please feel free to tell me so.

These questions are in a jumble no doubt, I'll try to structure them as best I can to flow.
Where are the physical dimensions for them? Neck, tail, body length, wingspan.. that kind of thing? I haven't cover-to-covered the book so I might have just missed it.
Largely up to you, with GC approval (Everything is with GC approval so I won't bring it up again.) Your dragon can look like whatever you want. The one in the rulebook looks mostly western but really the only things that matter are the parts that interact with the rules. You have winged flight and no usable hands.
I went Monster Specialty Martial Artist and will probably take Dragon Lord for progression. I'm trying to play 'critter as the class' as close as I can and those seemed the best fit. Any other classes that jump out? Soldier seemed interesting but looked like there were too many things that required armor to be of use. This may just be a perception thing though.
If you're looking to be a combat monster with natural weapons, it's hard to go wrong with the martial artist. Soldier isn't bad either. The beast upgrade will let you use armor. Just style it as plates or padding over the more vulnerable areas.
You said you want to play "critter as class" but dragons were much more than just combat monsters. You could be a courtier or a sage and be a great dragon.
Paddyfool's thread on Breath Weapon feats will help out a good bit along with both tricks from that same thread. I plan on making grappling a focus for the character so Grab'n'blast'em will get some mileage. Any others that spring to mind? The two feats that modify your natural attacks are neat. One adds qualities the other upgrades their rank. The feat that upgrades rank only looks able to take once. Any other ways to upgrade natural attacks I'm missing? DLord has some action there as the lvl3 benefit.
I am a fan of those feats but I really think your first game should be pretty close to the book. Save stuff from the board for when you have a better feel for how the game balances. This is of course only my opinion.
How would you handle Draconic Legacy being taken by a Drake, btw? That's one of the first level DLord benefits. The attribute bonus fits, but what of the breath (you already have) and flight with the resulting penalty? Assume the new flight speed?
Probably the best way is to just suck it up. It's not the best benefit for a drake but it's not that bad. The way it's worded, if your breath weapon is something other than fire, you'd gain the ability to breathe fire or your normal type (IMO) and a 20 ft speed bonus is a nice option.
Optionally, your GC might let you pick a different species feat but I don't think that's needed here.
I'll leave it at that for right now, time to go watch a movie with the wife-unit. I had hoped to put more thought/research into this and ended up hammering it out. heh
Good luck with your first game!