Installing a WP site on MAMP

I have been asked to Redesign a wp site for a client, So I’m not interfearing with their day to day running of the site i tried to install it locally, Now I tried first with a fresh WP install and that worked fine. So i Downloaded the site from their FTP and installed it on MAMP (more information) but when i launched it I got no content and no styling and just a basic 20-10 theme, after a lot of messing around I got the correct theme back but no content so I exported it from the live wp site and imported it, (website)I got the content but completely random css styling. Am I doing something wrong because although I’m new to WP .php if they work on the ftp fine why shouldn’t it work on the localhost ?
Any help would be great