Im making a site using Foundry
My client has requested headers and menu in Imperfecta Font.
Do I load this font into my project … which means that all website viewers will load it?
Or should I encourage client to pick a Google or Typekit font?
Does it slow down the site?
When does back up font come in to play?
I’m not familiar with the font Imperfecta. If it’s available as a web font and your client wants to use that font, then I don’t see any reason not to.
You would use the Typeface font and add it as a self-hosted font. All users will download it from your website, just like they do any pictures/graphics, etc. Yes, it will slow down the site slightly, but most font files aren’t huge, so it shouldn’t have a noticeable impact on speed of the site. It’s really no different that using a Google font, except that it’s served from your server and not Google’s.
I started to reply and I got side tracked and @DLH got his reply in first. 
If we assume the license for your font allows for web embeds then you’re good to go using it with Typeface as @DLH points out. It shouldn’t appear to work any different than a Google font, and as a plus it will be served from your own server so as long as your server is working the font is working. The same can’t be said if a CDN like Google Fonts were to be down (even though that isn’t very likely). It also means your font loading is definitely GDPR compliant if you’re in the EU and that matters to you.