Wordpress website health check

We had a serious crash through a rookie mistake. At the same time unknown to us our DB backups weren't happening and when we tried to restore we had no luck. Fortunately we had an image backup although one month old it nevertheless got us back up.

We built a new server and blew back in the image. Now the website is very slow and sometimes non-responsive. This was not the case before.

I need to know what is causing the problems and what it would take to get it functioning perfectly again? After the diagnosis I can make an informed decisions and look to find the budget to get it fixed.