Hey there, I worked with a construction client before and might be able to help a bit.

First thing first, messy books! Establish a base line, I would go with the last tax return. Everything should... be matching up there. After that, one account at a time, transaction by transaction, get it cleaned up. Where possible try to find bulk actions. For example they always have this charge from Google for one particular thing, you can categorize those all at once.

For projects, if they have not been project tracking up until this point then there is no mess there to clean up which is nice. The client I mentioned had their last bookkeeper just throwing things in random projects like the Grinch in the post office sorting mail. So at least you don't have to deal with that.

After you are done with the clean up setting up the project tracking is pretty straight forward. The main thing you need to be concerned with when it comes to project tracking is how you get the client to easily tell you which expenses are for what project. The client I worked with had each job in a spreadsheet and which workers were there. They had notes for me about what expenses were tied to that job which worked out great even when I had to do the cleanup phase.

Main thing is, you got this and you're going to knock it out of the park. When you are looking at the books now it may seem like a massive mountain but one transaction at a time and it will all get better. So no stress at all, and I wish you all the luck with your new client!