I didn't read all of the post, but the guys are absolutely correct about wheels. Wheels certainly have weight limits, and you don't necessarily have to weigh as much as 300lbs to start worrying about wheels. For some wheels, 200lbs is enough to cause concern. It will depend on the type of wheel to some extent (a lightweight race wheel for a road bike will have much lower weight recommendations than other types, for example). A thicker metal rim and a high spoke count will definitely be good for a skinny (but not super skinny), sporty wheel. Basically, it's a safety issue. You don't want to be breaking spokes and having maintenance problems with the wheel. The last thing you want is for a broken spoke to turn into a serious crash. I would listen to them on this point. Yes, more durable wheels may cost more.

As for the frame and type of bike, go as sporty as you want. Faster will mean a skinnier wheel rim, a lighter frame, and straighter tube shapes (i.e., not a step-through bike).

It's good to go in and learn about all the different types and make the information-gathering trip you did. Now do some homework and then go back ready to test ride some. Try out other shops and do the same.