2nd install for different site on different host

I have successfully downloaded WP and created a website. For this i went to a host and downloaded WP there. All went well. Now I want to do it again for a different client who currently has an old WP site that i am to replace, once I have developed it. The 2nd client’s site is on a different host to my first client. What is the best way for me to start with the 2nd client? I don’t know if I should download WP from their host, or if this will wipe their current website? Secondly, do I need to be aware of any risks that could affect my first client’s site? Thanks in advance for you help.