So I've never really toyed with the advanced rendering options in Bryce....I was wondering if you guys could give me some pointers, some suggestions.  Anything would be appreciated.  Thanks in advance!

For a really good final render pass, you might want to try using SOFT Shadows, especially in you have say an indoor-nightime scene  that's low-lit. Checkout 'Lack Of Imagination' in my gallery to see what I mean. 
I compared my actual desk lighting to my render and realised that the shadows on the wall were too harsh. Soft Shadows in the RENDER Options d/down fixed that.

I'm sure others will be along shortly to add something....

Available on Amazon for the Kindle E-Reader

All the Woes of a World by Jonathan Icknield aka The Bryster

And in my final hours - I would cling rather to the tattooed hand of kindness - than the unblemished hand of hate...

Raising the Quality settings in Bryce can get expensive time wise.
Lighting, reflection, HDRI / IBL, Heavy texture mats, Heavy Object content, can all play rolls in a lengthy render. Keep your end result in mind and work it from that angle. If your entire scene is rather simple and you want a super quality, then by all means experiment with setting the bar higher. On the other hand when you've created a complex scene, you can rely on details in the scene to compensate for super fine(clean) renders.

Lots of variables like post work and multi-layered renderings(multiple renders layered together in IE: Photoshop)

I usually test my renders using smaller resolutions, then increase the size for the workable piece. Then composite and postwork in Photoshop.....Other people do not care for post work.

All personal preference & Lots of practice.
Have fun
ICM

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Ockham's razor- It's that simple

Like ICM said, it is all about balancing act of several things.  I have better going building a scene rendering regular and no AA. I prefer document size 810X607 initially.  Other peeps like different sizes initally.  As the scene develops I may change to regular with AA turned on and plop render in bits.  When it all comes together I may go to superfine and plop render a few sample areas to see if the higher setting is worth the longer wait.  Finally I increase document size and do my final render.   

One quirky thing I didn't discover early on with B5 was that saving the rendered image as jpeg created terrrible aritifacts.  I save image as .tiff now and convert to jpeg in post work. 

B6 has different jpeg settings but I haven't explored them.  I'm happy saving .tiff.  I played with fine art setting once or twice but my aging eyes couldn't see a difference.