Clipless pedal and shoes??????

Clipless pedals are the best investment you can make on your bike to improve efficiency/speed.  Don't know if 1-2mph is accurate, but it will help.

Carbon-soled shoes are supposed to provide better energy transfer from foot to pedal, but most of the advantage can be realized just be getting the pedals and a pair of shoes that fits.

As above, the best tri-specific shoe is the one that fits your foot.

I'm new to clipless and have only worn one pair of shoes but I really like my ________.

See, it doesn't matter because they are your feet.  I went to a LBS and tried on a bunch.  I was surprised to find out that:

1.  Only one brand felt comfortable on my feet, the other two they carried were painful - and I would have ordered one of those if I hadn't checked it out first.

2.  The sizing conversion would not have worked for me.  I was able to figure out what size was just right for me.

Then I went home and ordered the shoes from Trisports.com with my BT discount.  I love 'em.

p.s.  I went with $25 Motobecane pedals from Ebay but spent over $100 on the shoes because I figured that comfort was most important.  Turns out the pedals are great for me too, they have more than enough float for me which seems to be a big thing people rave about in more expensive pedals.  I don't consider the weight difference much of a consideration. 

Did you see any significant speed increases over using running shoes??

Well, at the same time I also went to aero bars and trained a lot over the winter so I don't know how much of a speed difference I can attribute just to the shoes/pedals.  I'll say this much (just my opinion on what's working for me).  I hate being on my wrists for a long period of time on the bike so the aero bars not only put me in a better position to ride faster but allow me to ride for longer periods of time.  When I lay down in aero I just feeeeel the difference.  I don't feel it like that with the shoes/pedals.  I know they make a difference, I just can't explain it like I can with the aero bars.  I'm still a masher (form wise not gear wise) so I try to concentrate on the full pedal stroke and that's when I notice them the most, but when I ride and my brain wanders (frequently) I don't notice them at all and I think that is a sign of how much they help.  I don't know whether I would rank one change above the other, I think you should do both if you can. 

I already have aero bars and have removed all of the spacers from my front end...I think that helped quite a bit, especially going into the wind