On the amp/effect side, what would be good for a thick lead/solo tone (a la Steve Vai, Satch, etc.)? I was thinking about adding mids/bass, knocking down treble a bit, and throwing in reverb and a little delay. What pedals would you guys recommend for reverb/delay, or what other sorts of suggestions would you make?
Ibanez RGA121 | ESP LTD H-1000
Axe-FX Standard
By the way, I believe you're after a delay, playing live with reverb makes you sound less clear. Is it just gonna thicken up your tone, or dyou want more from it?
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Would the reverb contribute anything for home recording/home practice? I don't plan on playing live any time soon, I'm just looking for a thicker tone. But yeah, I was pretty sure that I'm after a delay.
Ibanez RGA121 | ESP LTD H-1000
Axe-FX Standard
I would go with an EQ because you can add the specific frequencies you want.

Maybe add a reverb or light delay to give yourself some breathing room, give it a more open, less compressed sound.
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check out the delay pedals i suggested. the DL4 is awesome (i have one, and i'm never getting rid of it), and the Nova is revered as one of the best delay units money can buy.

to thicken up your tone, try:

closed back cab, V30 loaded
boost (maxon od808 is great for this)
hotter, smoother pickups (SD SH-5, for example)