Since I installed multi-site I have the following problem:
First time visitors to my homepage http://www.oeivoorgroei.nl are redirected to http://www.oeivoorgroei.nl/wordpress/wp-signup.php?new=oeivoorgroei.nl
After once clicking 'home' and opening the home page, visitors are not redirected anymore.
How can I solve this such that first time users are not redirected?
The issue is that your install is seeing oeivoorgroei.nl and http://www.oeivoorgroei.nl as being different. So there is either something in your .htaccess or in your WordPress settings that are seeing it as two different domains. It is looking at oeivoorgroei.nl as a domain that does not exist and need to be registered. I've only seen this with a domain mapping plugin, but I am assuming you are not using a domain mapping plugin for your main site.
Moved to Multisite, since that's the only way you'd see this one...
You cannot have MultiSite installed in a subfolder while 'acting' as if it was in root.