Presumably you have some sort of patch-panel area in which you're terminating all this, either a proper panel like this one or by putting male 8p8c ends on all your cables.
Aside: I recommend the patch panel, as it's then easy to convert any jack to a phone jack if you should need such a thing, or use it for any other signal you need to move from one point in the house to another...a patch cord plugged into 2 ports gives you an electrical patch from your bedroom, say, to the television set
I would then recommend any 802.11af PoE-enabled switch with an appropriate number of ports. Gigabit obviously is the recommendation there, and you already have all that cat6. A caveat: PoE + Gigabit switches are expensive. Depending on how many items other than your cameras will need it, you may be better off going with something like a PoE injector versus a whole PoE enabled switch. Add that to an appropriately sized gigabit switch (the Netgear GS108 is good for a few devices, something like the JGS524 gives you up to 24 ports) and you will have a very respectable home network.
Note that you are not yet connected to the Internet with your home network, you need a router. Depending on your level of comfort with networking and tinkering, I would recommend a Linksys WRT54G reflashed with DD-WRT firmware if you want some 'build-it-yourself' cred. As Neil Krawetz put it: 'DD-WRT takes a $20 router and turns it into a $500 gateway.' This could enable all manner of fun things, like letting you view your home security cameras with your smartphone while out of the house, etc. If you're not comfortable with that level of hardware tinkering, the WRT-54G is still a respectable unit for home use. Alternatively there are many others like the Netgear WNR1000. When it comes to routers, as long as you're not tied to letting the LAN port requirements dictate your choices, you have as many options as you can spend time Googling for.
Which leads me to explain why I would recommend a separate router, not an all-in-one unit: you want the best switch you can get for your internal network, but almost all internet routers are equivalent until you start hitting some pretty major price-points. You want to get the most bang for your buck, so get a decent gigabit switch, maybe support for VLANs and/or some other management capability, and then just add a router to connect you to the internet. Your router/gateway device (depending on the choices you've made) will handle the addressing and the connection to the 'net, while your local devices will all be able to take advantage of the cat6 cable you've installed.
As for the cameras and software, I agree with Linker3000's recommendation for Zoneminder. And definitely look over the HCL for Zoneminder. I'd recommend making a scaled diagram if you haven't yet, and make sure you figure coverage angles and distances before you start purchasing. It will make it much easier when you're looking at the 64 degree angle of view listed on a camera and wondering if you'll be able to see the shed at the same time as the corner of the house. It's a significant amount of work, true, but this is the type of project you do only one time (per house, anyway...;) ) and you want to make sure you get it right. Planning is the biggest thing I've seen my clients not do that requires me to come later and fix things.
tl;dr: Get Gigabit PoE injectors, a good managed gigabit switch, and a DD-WRT router, then use Zoneminder. Make a good plan first.