Currently, I’m using my http:// tech-rage.net domain for my website(which I’m updating). Should I use this same domain, create a sub-domain, and set up my Nextcloud server? In this case I need to purchase a SSL certification, right? Oh, my VPS is through Inmotion Hosting.
There are no downsides to using a sub-domain for nextcloud, this is what they are meant to be used for. As for SSL encryption you should look into letsencrypt, they will issue you with a free certificate to use on your site: https://letsencrypt.org/
Go the route @MichaelLindman has suggested, Letsencrypt are excellent and easy to use. A subdomain is also a good idea. You should be able to setup letsencrypt on your nextcloud box to autorenew as well.