If I take a personal hosting accound is Wordpress already installed or do I have to do it myself?
You can choose when you set up your service.
Most of the hosting provider companies facilitate their customers with already WordPress installed services while some are not providing this service. By the way, installing WordPress is not a difficult task. I also installed WordPress on my fastlabourhire website by myself. When you integrate your domain with hosting, there will be an option to install any CMS like WordPress, Joomla, etc. Click on WordPress and it will install automatically.
If you face any issue just let me know I will guide you