I need help matching parts
I don't think I'm going to answer all your questions, but ...

First, you are talking about unisolated circuits connected to mains. You should assume that any part of the circuit can carry lethal voltages at any time power is available. You say you have done electrical work, so you should already know something about this, but most electrical doesn't require the kind of debugging this circuit might/will require. Be sure you really understand the safety issues before proceeding with this project. 


  picMicro chips running at 5v. That means the output pins will be at 5v, right? But the max gate voltage for any of the triacs on digikey are 2.5v.


A current-limiting resistor would probably be enough to reduce the drive to something the triac could withstand. But you'll probably want to add opto-isolators anyway (see below), which changes the whole problem. 


  ... it [L6004L3 triac] uses 3ma gate current, but am I reading the data sheet right that it could draw up to 1.2A at the gate?


IGT (gate trigger current) and IH (hold current) are the key parameters. IGT tells you the minimum current needed to trigger the triac into conduction. IH tells you the minimum current needed to keep it in conduction. Also note figure 4, which shows how the trigger current varies with temperature.

The 1.2 A figure is the abosolute maximum peak gate trigger current. It means that if you provide more than 1.2 A, even momentarily, you could damage the device. It's up to you, as the circuit designer, to ensure that you never provide more than 1.2 A. Even better, design in a safety margin and never provide more than, say, 100 mA.


  Also, that triac isn't opto-isolated, but still appears to be isolated to 2500v? If that's the case, do I need an opto-isolator?


From my reading of the datasheet, the key indication is the note on pg 57 (the drawing of the "L" package). This says that the package has an "isolated mounting tab". A different package has the tab tied to the center pin (MT2, which would be a hot wire).

I think that means that what is isolated in the L package is the heat sink tab on the back of the package. This would allow you to bolt the part directly to your case and not electrocute anyone who touches the outside of the box. (But I'm just reading between the lines of the datasheet --- do you really want to trust your life to some guy on the internet?)

It doesn't mean there's any isolation between the gate and main terminals and it doesn't mean there's any protection for your digital circuit or for anyone debugging the digital circuit. 

My advice is, use an opto-isolator between the digital circuit and the triac.