Apache will always reply with the first certificate in the first <VirtualHost> section if it gets a request for a hostname it doesn't recognise elsewhere. This is troublesome if the hostname entered by the user is different from this default hostname.
But I'm not sure I see the problem: most users will just type in the hostname, without the https:// in front of it. 99,99 % of the time, it's the webservers maintainers responsibility to redirect HTTP to HTTPS. If you're just redirecting for one domain, then other domains shouldn't be affected.
Also, the following is redundant:
If you have Apache 2.4.8 or above, then SSLCertificateChainFile is deprecated and having SSLCertificateFile point to fullchain.pem is perfect. If you have a Apache version lower than 2.4.8, then you should point SSLCertificateFile to cert.pem and SSLCertificateChainFile to chain.pem. I'm not sure if Apache <2.4.8 will understand fullchain.pem if entered in the two directives.
The clients browser. Normally, it will choose HTTP, unless you've set a HSTS header or HSTS preload. Any redirect to HTTPs will be done by your server otherwise, if you've set that up of course.