There's nothing wrong with the logic level mosfet approach, and it may be easier sometimes. Each approach has its plusses and minuses. For turning on an LED, either approach will certainly work, and the mosfet might even be easier. But if you're careful about limiting inrush current into the gate capacitance, you need a resistor on the gate, so the final parts count ends up equal. I'll stick to the original NPN approach for now.
I'm still a little confused when it comes to selecting one on digikey
Understandable: Here are some rules of thumb to narrow down the process
1. For semiconductor physics reasons, NPN generally works better than PNP, so choose an NPN transistor by default, unless you have a reason to choose PNP. (See the TV-B-Gone for an example of a legitimate reason to use a PNP transistor -- it's used to switch a bunch of NPN transistors, and doing it this way spreads a large current load over many transistors).
2. When digikey presents you with too many choices, click the "in stock" button and sort the list by quantity available. This will give you an idea of the popular general purpose parts versus the rare esoteric devices. Take the precise rankings with a grain of salt of course, but unless you know you have a good reason to do otherwise, you probably want to choose a part that's reasonably high on the popularity list.
3. For general hobby use and ease of breadboarding, you probably want a TO-93-3 through hole package, so a filter on that will eliminate surface mount devices (if you're mass producing via automated assembly, or if you want the tiniest miniaturization, go with SMD).
4. As a general purpose NPN switching transistor, you won't go far wrong with a 2N2222 or 2N3904. Choose one, buy a hundred for your parts bin and you're set until you have unusual requirements.
Don't let any of these general shortcut rules discourage you from downloading data sheets, reading them, and understanding as much as you can. Data sheets are your friend, and learning how to read them will be very helpful if you want to progress from the "tinkering and hacking" stage into the "understanding and carefully designing" stage.
For the specific parameters you asked about:
The ce breakdown voltage tells the maximum voltage the transistor can handle between its collector and emitter without letting out smoke. This should be comfortably higher than the maximum voltage your circuit will present between the collector and emitter. Most general purpose transistors will be able to handle 30V or more easily, so unless your supply is higher than this, you don't need to worry about it.
"Vce saturation" tells you something about how ideal the switch is. When a transistor is fully "on" (in saturation), to a crude first approximation, you might think of it as having the collector and emitter shorted together. But to refine this crude approximation, you can think of it as the transistor maintaining this "Vce saturation" voltage between the collector and emitter. (You can still further refine this crude approximation by looking at the data sheet). The remaining parts of your load will only see your supply voltage LESS this Vce saturation voltage. This may become more important if you're running at a low supply voltage.
