Public IP addresses are not fun to send people and even less so if they are not static, assuming you do not have a static address then get a dynamic DNS server. Dyndns were formerly the de facto standard but they now want a credit card and cancel after the first month to get the free service so might want to shop around.
If you do have a static address or a nominally static one you can just fiddle with the DNS options for a domain (don't run your own DNS at this stage). The dynamic DNS services will tend to want money for them to support your own domain but you can get around that by setting a cname entry in your DNS (I prefer cnames but you can do forwarders as well) and point it at your dynamic DNS provider domain, this does of course include the option for no subdomain and the www subdomain which is what most people will call the internet.
Yeah. I was really wondering about how I can change ###.###.###.### to something like www.sitenamehere.com and if that had anything to do with the tedious DynamicDNS, especially since my internet is run off a router. I might end up ruining the internet for everyone else who lives in the same roof as me!
You don't, you need to buy a domain (it's cheap) and redirect it to your IP.
Also keep in mind that your internet will be awfully slow (Usually 1MB/s in upload) when compared to what a specialized webhosting can offer you (100MB/s up to 1000MB/s).
This means that the visitors on your site will download stuff at an abysmal speed. And pray that there aren't more than 5 downloads at time, otherwise they'll download even slower!
Speaking of server stuff, do you think i could connect my computer to other servers using wireless connection if ever i plan to upgrade the website, but keep my computer?
Wireless connection isn't good for this kind of stuff, it's really really slow (except if things you're going to connect are really near and there aren't any interferences at all) and servers need to communicate at uber-fast speeds.
Also, if there are people on your website doing stuff (uploading, downloading) the internet in your house will be SO slow that it'll be unusable.
Just go for a cheap ($50 yearly) webhosting, it'll be AGES better and cheaper in the long run, considering that you'll pay more than that in electric bills to have a PC on 24 hours on 24.