I'd like to keep the joists and posts.... I would also consider replacing the joists and posts, but I'd rather not, as they seem both solid and functional.
One question is - are they to code? You will almost certainly need a building permit for the repair, so what will matter is what the inspector thinks.
If it's an attached deck, and the foundation is not below the frost line, you'll need new footings. Hope you don't have to dig out the footings to prove they are deep enough. I've seen it happen.
Also, if it's not at the desired slope (it should be gently sloping away from the house), then even with solid and functional joists, you may want to replace them to get the slope right... in order to keep water away from the foundation and smoothly flowing off the deck so the wood doesn't hold too much water and rot the decking.
I've never built a deck before, and I think it'd go a lot more smoothly if I had someone there to guide me (and save me from making rookie mistakes).
That's true of any project :)
The ledger board is particularly interesting to get right - different foundations to adapt to, so really having someone who can come over and look under the house (assuming a ledger board exists and it needs to be replaced) is well worth figuring out how to accomplish. It's also basically impossible to put on alone, since you need one person outside and one under the house.
One option would be to volunteer a bit for Habitat for Humanity. I've assembled a few decks that way. If they have a skilled team leader, the deck can be almost done in 1 day (close enough you will have the idea), so you can see the entire process (minus the footings, which are typically their own project day - and usually the railing isn't completed the first day). You can also try to have a discussion over lunch with one of the experienced volunteers, house leaders or the site supervisor to get more insight. They have the building code on site and you might get them to walk you through the things to watch for... more "developed" Habitat chapters will even have a "training manual" or "key punch list" for each part of the house, and that may be on site as well. That would give you a step by step guide or list of key things to watch for... so you would know how they do it and what they train their leaders to watch for in order to ensure the deck stays functional and in code.
As a note, in my area, they are rather careful about when they time the deck construction, so that they know they have an experienced team on site (most are done Wednesdays, if I recall). It's considered one of the harder portions of the house to "get right". Of course, if it's a stand-alone house, they can't really time it that much, but when they are doing a development of multiple houses, the deck is one of the areas they "nudge" (put people on projects in other houses and delay the house with the deck slightly) to get their team of regulars doing the work.
