I want to eventually have my home wired with poe IP cameras tied to a dedicated computer DVR. But instead of going all in and hoping for the best I would like to put together a simple single camera systems to learn on and add upgrade as I become more sure of what exactly I want and how it works.

What I have -

Computer
Belkin ac 1200 wireless, well once I figure out how to get it to behave
Hard drive dedicated to just the camera

What I do not have -
Internet connection. Have to use a cell hotspot because att are dicks.
Camera preferably or of some kind and a maybe an independent illuminator.
Poe Ethernet switch
Software to run cameras.

I'd love to be able to get this thing running in a way that I could access the camera from anywhere in the house mostly with a phone or tablet. Looking for some specific recommendations for starter gear that won't upset me terribly if it dies. And anything I'm missing.  Amazon search results were a little overwhelming without knowing what to look for.

Tag for recommendations as I'm in the exact same situation. No Internet connectivity out here other than Hotspot on my Verizon phone. Our house is currently gutted so I know now is the time to run poe cableso but I haven't figured out what type or where to for a pc based ip camera system (running blue iris I think?)

So far I plan to run 10 drops of Cat6 for home network and another 12 to run PoE for IP cameras. I plan to employ a dedicated computer with Blue Iris to manage the cameras.

I plan to run all the lines to a single room in the basement.

I guess a question I have is would I need a separate network switch as well as a PoE switch?

If I'm understanding your question, you do not have to have a separate switch assuming you currently have enough ports on your router to accommodate 12 runs of CAT6 to the cameras.  If not, then yes you will need a switch(s) that has POE built in for each camera.  You can also use non-POE switches combined with POE injectors but it's no cheaper and requires a lot of patch cables.  

Be sure to use good quality CAT6 cable, solid copper wire not copper clad.