Congratulations first off all! It's always much more rewarding when you get something done without too much help, he? You can get a Serverlist.cs that is a somewhat more forgiving when you change IP numbers a lot at:
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And you should get a dynamic DNS supplier:
No-IP - Dynamic DNS, Static DNS for Your Dynamic IP
It will allow you to map a DNS name to a often changing IP number.
(Like Aryvex.gameserve.com == Your IP number)
If you mean 'Your PC' as the single PC you use for general purpose AND hosting a RunUO server, don't expect it to accommodate a lot off players.
Usually a dedicated machine is used for running a game server and it will be a high speed machine, lots of RAM, fast Disk, fast Ethernet and fast (and reliable) connection to the Internet. It will be stripped of all non essential services purely to accommodate the Client.exe.
Nevertheless, if you simply wish to experiment a bit, and your PC is not an antique one. you probably can have 5 to 10 players online. (I did once).
Do close all non essential background processes, services, scheduler etc.
Good luck!