Power supply time!

[guitarmonky55]

So now that my radio shack has all electronic components, regardless of what they are, for $0.20 (yes that includes the assorted packs of capacitors and even the transformers and such...everything!) im absolutely LOADING UP!  i bought a bunch of their 300mA and 1.2A transformers for 20 cents a piece and nabbed about 20 lm317 power regulators.  Seeing as I've been meaning to do a regulated supply for quite a while, this seems opportune.  Ive been looking at the schematic for the ultra clean PS from GGG http://www.generalguitargadgets.com/diagrams/ultra_clean_ps_sc.gif and I have a few questions before i fire up the iron.

now my first is that im using a 1.2A transformer and the lm317 says it can handle up to 1.5A of current flow...so basically I can power as many pedals from this thing as I want so long as I dont exceed the 1.2A limit of the transformer right?  I know thats a dumb question, especially since ive taken enough physics classes to know that should be the limiting factor here, but I wanted to double check with people who know from experience.

second, I had a few questions regarding the schematic.  It calls for a transformer that puts out 25vAC on the secondary, mine does 12.6vAC.  Seeing as Im stepping everything down to 9v with the lm317...wouldnt it be better to be running it at a lower DC voltage when it gets to the chip?  This means less power dissipated as heat, which means more of the cooling process from the heat sink can be used to handling larger current draws right?  For the lm317, how does the input DC voltage affect the performance?  Do I need any part changes or can I still use a 240ohm and 1.5k resistor to get my 9.06v?  Im pretty sure I should still be able to use the same resistor values but once again I want to double check.

Thirdly, I wanted to address the purposes of the 1000uF and .1uF caps that come after the rectifier diodes.  Are these what are referred to as the filter caps?  And if so, does increasing/decreasing their value affect performance, particularly in regards to the cleanliness of the power supply?

Ok and last but not least...I was working with a smaller transformer in a headphone amp(the 12.6v 300mA from RS) and the said capacitors above proved to be quite a PITA to discharge every time I unplugged...so I put a resistor across them to bleed off the charge when I powered off.  I know this is standard practice in guitar amps with the big caps, but In the case of this power supply would it be a bad idea to go ahead and add for that extra measure of safety when Im working on it?

Sorry for all the fairly simple questions, I just wanted to re-affirm everything before I dig in on this.