Excuse my technically incorrect explanation. I'm stating this from an artists perspective and don't know all the math behind all of it. :P
Glass uses a lot of processing power, and there's really not a way to render faster. I can however suggest a few things that will make the glass look better.
This is probably the biggest issue I see when glass looks dark and yucky. Glass refracts/reflects light all over the place. Glass doesn't really hold much color itself. It's mainly just a light-bender. That's what gives it a realistic look.
Use an Environment Map
As stated before, glass just bends light. The more types of light it has to work with the better. Environment maps are one of the easiest ways to make glass look realistic. And it's not too much work to put one in the scene.
Set the color to White
Setting the color of the material will tint the glass with that color, so if you leave it with the default "almost white" grey, your glass will be darker. Set it to full white to have the maximum transparency.
You do need caustics
I don't know exactly what they do, but I know it has something to do with light bounces. You need caustics if you want the light to go through the glass.
In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface.