Too bad you don’t live closer! 
I have read that could be an issue with composites… The deck does get sun and gets hot in the summer even with wood, which, besides cost, is a reason I have been leary of using it.
The house is U shaped with on branch made 6 feet ;longer than the other and teh deck fills in the center area. Here is the google earth picture:
With almost 3 sides enclosed and light colored vinyl siding to reflect the some back on it, it gets pretty hot with wood!
There is a seasonal screen house on the deck (just put it up last week) that is stored in a shed for the winter. The light colored ares other than the screen house are the tiles covering the rotted areas.
There is stairwell down to the basement, and although it is not clear in teh picture, the who area where the connection between outside straight sides end are angled and meet in a point… That whole angled area are were the stairs are… so not so simple… also the deck is fairly low to the ground and there is trouble with animals getting underneath that are so getting under the house (both sections on the left side are additions with a crawl space… the rest of the house has a full basement.
Always so not so simple… but even so just the boards
As for the structure… I don’t know… As I said it likely 30ish years old and i want it to last without issues for say 20 years (assuming teh house is sold within 15ish years)… I will have to rely on teh judgement of the contractor on that… But how can you find one you know you can trust? I keep hearing about home improvement contractor nightmares!
Given the deck is fairly low to the ground, if I go with pressure treated pine I would want top quality ground contact rated… But the color is not great… I keep hearing about teh tropical hardwoods like IPE but gather the are much more expensive.
About 5 years ago I got a quote from contractor that lives across the street from me for just the deck and it was about 30K… But he would only do Azek decking… And that put me off of doing it back then.
I would spend 10-15K on the deck as it is important for the house resale value, as well as enjoyment, but with an uncertain job, age and the fact the house needs a lot of other repairs/updates, it would need to be done well, look good and last because there es no way I could afford to redo it!
The railing are teh same material as the deck and looks lil they were build from scratch when the deck was built.
-Karen