I am looking around at some of the nodes for sale on ebay. I see some that are 5v and others that are 12v. Why would one choose one over the other?
The 12V nodes are really just 5V nodes with some type of voltage regulator. The primary advantage to the 12V nodes is that you can have longer strings without the need for power injection.
Also I see they are typically sold in sets of 50. What if I only need 25 or I want 125.. do you just cut and use what you need?
For the most part, yes. If you look in the WIKI under smart strings, you will see a link to some of the ones that Ray sells. He has different lengths and these are 12V. Before you buy any, you really need to decide on a controller or controllers that you will be using and then make sure that they are supported by those controllers.
What is the typical hardware set up using RGB.... For example I wanted a simple mini tree or mega tree. What would one all need hardware wise to make it function?
LOL, what sounds like a simple question has so many variables that it could take all night to answer. If you were to go with DLA equipment, you would start off with an EDT (etherdongle) flashed with Pixelnet firmware. For a minitree, you could use a smart string controller (SSC) and a smart string hub. If you pan on continuing to use the LE's, then you would need the active hub to provide the DMX conversion. For a megatree, you could use the Zeus which is basically a group of SSC's on one board. There are two types, the 8 and 16 which have either 8 or 16 outputs. As said before, this is just the DLA equipment. There is a huge number of these devices available now both DIY and commercial so if you can't find what you need here, there are many other options.