How to take over as administrator of a site containing WordPress?

I have been hired to take over the administration of a site which contains WordPress.

In the past I have always had a copy of the site on my localhost so I can test changes before making them live. In this case, all I have to work with is the live site itself.

What would you recommend I do in this instance? I have some ideas which I will list below, but I would appreciate some advice.

First. I’m wondering how easy it would be to copy everything: the site files, the WordPress files, and the database, over to my localhost. There I can experiment with any changes necessary before committing them to the live version.

Second. I could copy only the site and WordPress files from the remote server, to my computer, and then link to the live database on the remote server. I’m thinking this might be a good approach as the database will always be up to date, and I would not have to deal with creating a local copy of the database.
Having not tried this approach before, I’m hesitant. The last thing I would want is to accidentally alter the live site.

What do you think? How do you take over the administration of a live site? I appreciate any advice you can provide.

don’t you have access to hosting control panel to download files and database ? I think you can ask it from your customer.

I do indeed have access to the hosting control panel. However, I’m concerned about copying everything to my localhost for a couple of reasons. First, although only a portion of my customer’s site utilizes WordPress, everything I have read about making a copy of the WordPress database etc makes it sound like there is always the possibility of problems. Second, I can see myself needing to make a lot of changes in the future as well, and downloading an up-to-date copy of the database every time seems ridiculous.

I would like your opinion of the following:

I’ve noticed that as well as the primary domain folder: “”, there are other domain folders alongside the primary. One is entitled “”. I’ve never seen this before in any of my projects, but as I’m still rather new, I’m curious if perhaps you have experience with domains with the prefix “dev”?
Could this be to denote a development version of the website? I know this domain and folder are not being used at present, so I’m wondering; Could I place a copy of the site files in this domain directory, to use as my development environment? Since it is within the same parent directory as the current live site, I’m thinking this would utilize the same database as the live version of the site, thus eliminating my need to copy the database.

Have you encountered this sort of set-up before? Where there is a second domain folder and domain with the prefix of dev?
And, do you think my plan would work? Would it be the easiest way to have a development version of the site to test changes before committing them to the live version?

I appreciate your help very much.