So I'm trying to convert some at home servers into rack mountable servers to take up less space. I'm considering buying a cabinet that is 23.5" wide and a case that is 15.3" wide. Is there a way to install the case in that cabinet. I guess the main question is what is a good way to determine compatibility? Also where in your opinion is a good place to buy server cabinets and cases?
Are you asking if you can install existing desktop systems in racks, or how to install rackmount systems in racks? For desktop systems, you can can use rack shelves. That will result in a slight loss of space as the racks take up typically 1/2U each. However that typically isn't a big deal.
If you are talking about installing rackmount case systems in racks, you just need to make sure the two are compatible. Generally these days they are. Most racks have a square hole system and you use free-floating cage nuts to secure the servers. Here's an excellent rackmount tutorial from @StandaloneSA that should help answer some of your questions.
Newegg and several other retailers stock a decent selection of generic rackmount cases, if you want to move your motherboards into new cases. The quality of the cases are generally good, but I've found the rails that are included are often very difficult to mount.
You can also buy shelves that mount in standard racks and place the PC cases on those. http://www.amazon.com/dp/B0026TLCR8
Or, if this just for home, skip the expense of a server rack and instead use custom shelving. The inexpensive restaurant wire shelving offered at many big box stores works great, and it is actually used by many hosting companies in their datacenters. http://www.dslreports.com/forum/r8250887-My-new-server-rack