The setup of purchasing manager server edition is designed such that you would download the trial and follow the installation setup as described. You trial it for the period and once you’re satisfied you want to actually “buy it”, you then do so from within the server edition itself.
It is done this way deliberately to weed out those who are not capable of running a server themselves. If you can’t get through the installation and setup, then you’re probably best not running it at all.
The hosted version will suit your needs a lot better as it remains cutting edge, doesn’t require updating, has any and all patches applied and is constantly monitored with minimal downtime (I say minimal only because it is professionally hosted service and I believe there is an uptime guarantee. I don’t personally use it and so I can’t guarantee what the uptime/downtime is).
Having said that, I run my own server version and I have to maintain updates personally, maintain the network it’s hosted on, do snapshots and backups, maintain uptime in lieu of my ISP going down, or problems within my own network, server maintenance and upgrades and security patches as well as firewall NAT/rule management.
It’s not THAT bad, I’m just highlighting some of the things you need to consider you’re going to learn along the way. Not to mention the domain name side of things.
The cloud edition does allow you to use your own domain name and if that’s all you’re after, I’d suggest you just do that. It will save you a lot of headaches!