Since you don't know whether or not you need shared or a dedi, I would say that your not capable of setting up a server at your house. No offense, just "judging a book by it's cover"... If you were a techy geek that knew how to do that, then you would know what you needed, hence this thread never would have been created.
If you did choose to setup a server at your house, I would recommend building (or buying) a decently spec machine. An intel quad-core at least (unless you already have a dual core laying around or something), at least 1GB DDR3 RAM, and 100GB SATA hard drive. I know, SATA drives you wont find exact 100GB, just saying at least. While you wont need that much, at the price of drives, just give yourself moderate room. 1GB RAM is plenty for Linux, but if your going to go the Windows (I don't recommend) route, then you would want at least 2GB ram. My recommendation would be Linux because windows sucks for servers, and use CentOS 5.x or greater. 32 or 64 bit doesnt matter, just depends on what processor you have in your rig. You would then need to install apache, php, mysql, phpmyadmin, and a few other things.. There are tutorials laying around. -- If you haven't used linux before, then save yourself the stress and forget it. I just posted this because it might be useful to you someday, or to someone else here.
Using your own home internet for a server, leaves you open to a lot of issues though. If you are not on a static IP, when your IP changes, your sites will be unreachable and you will have to repoint your nameservers. Which takes hours for it to work properly all around the world. You don't have and decent firewall protection. Real hosting providers, use high end firewalls. I see now, many advertise they are DDOS protected by Cisco Guard. So your talking like what, a $5k or $10k firewall.. Not sure the exact price. So your missing superior security that many hosts have.
Now onto Shared vs VPS vs Dedi: I personally prefer a VPS or dedi. You have full control over a VPS because you are given root access. A vps is basically a mini dedicated server. You share the CPU (processor) with the other handful of people on the server. They generally don't put nearly as many people on one VPS server as they do shared servers. The good thing with some/most VPS hosts, is that you have unlimited emails per hour, where shared you usually have around a 200-500 emails per hour limit. So if you are doing email marketing, kicking out to a list of 10K people is a pain in the butt and they will get on you for mailing. Interspire can throttle, so you could send to a list of 5k people at 300 per hour (or whatever your limit is). It would take a long time, but shared hosts usually don't put up with it. I have came across VPS hosts that have unlimited emails per hour, and others that have a limit. Just hit or miss, so contact their support and ask before ordering.
When mailing on a VPS or a dedi, it is good to first check the IP to ensure it isn't blacklisted. If you have already used your domain to mail, ensure the domain isn't blacklisted. If your good there, then ensure you are properly handling bounced emails. Interspire does this. Also it is wise to get on as many feedback loops as you can (yahoo, gmail, hotmail, aol, comcast, road runner, att, ect.) This way, when people click spam (instead of delete) you will get notified from the feedback loop. You then can remove that person who clicks the spam button from your list, and I add them to my blacklist so they definitely will not get anymore emails no matter what. This helps your email relationship with the hosts good as your taking care of complaints. DO NOT import purchased or "borrowed" or scraped lists. They are garbage and will get you into trouble! No repectable marketer does this. Scammers and people who have no real talent do this.
Another reason to get a VPS or dedi... While someone mentioned hostgator can handle 4k visitors, I beg to differ. Hostgator used to be good, like 4 years ago. NOW, they are garbage. Their servers are slow compared to what they were before, and compared to other decent hosting providers. I will give them, that they have amazing support (phone, support ticket, and their server techs are good). They are nice, and quick, and 24/7. They are anal about emailing, even on a dedicated server paying $375 a month! I provided proof of optin like at least once a month. Just a pain in the ass. Their servers are now crowded, and I have heard more and more of people getting a blacklisted IP address. My advice, is if you were gonna get hostgator despite my review here, then get their middle package. The smallest one is for 1 domain only lmao, their biggest package offers the same as the middle one only you get a 1800 number and a few other things nobody ever uses. They 1800 is good for a very low amount of minutes, after that you have to pay. So its practically useless unless you want to monitor how many minutes your using. So their middle shared hosting package is the best pick imo.
If you want a pretty decent VPS - check out SolarVPS
If you want a great dedicated server - check out SingleHop
If you found this post useful, and want my affiliate link for any of them, send me a PM. That would be kind of you. But I am not trying to abuse this forum, so I leave that to you. If you wanna be kind, cool, if not, oh well Im not worried about a few bucks anyways.