How do I get better-sounding vocals for voice recordings?

How do I avoid pops due to plosives and esses (sibilants) in voice recordings?

While you could use a pop filter over your microphone, or apply digital filters to edit out the pops and esses, I've found the simple technique of speaking off-axis with respect to the microphone works much better. You do this by pointing the microphone at your mouth, but you face slightly to one side of the mic so that you're not breathing or talking into the mic. You should use a directional microphone to get the best results.

How far should I place the microphone for my voice recordings?

The closer you place the microphone, the more intimate and quiet your voice will sound. The farther away, the louder you can speak while still sounding natural. Also, moving the mic closer will emphasize the bass in your voice. While you could use the EQ in post-production to get more bass, you'll also increase the bass noise that way. 

How can I get better sounding vocals with a different microphone?

Your best choice is a condenser microphone, but they are expensive. For a reasonably priced alternative, try a cardioid directional microphone or a dynamic mic with a clean mic amp. Dynamic mics tend to have more noise, but some people prefer their sound. A good digital recorder with a built-in mic also works great. The only issue with these higher quality microphones is that you might want to simulate the sound of a dynamic, which you can do using EQ to do a roll-off filter which removes the very high and very low frequencies.