Bike shoes?

They will probably make your bike split a little faster and your T2 a little longer. You have a month to get used to them so that's probably enough time. Keep them loose (spring tension) and try them out on your trainer first. There are lots of good shoe/pedal combos out there. I have Specialized TriVent shoes and Shimano Ultegra pedals.

I would think it is plenty of time to get used to them.  It would simply be a matter of riding a lot to get used to clipping in and out.  But, Be ready to fall!  Everyone does and it happens at times where it can be most embarassing!!! haha  I don't know the exact percentage but i think you could improve your pedal power up to 30% with clipless.  Once you go clipless you never go back!! :-P

I use speedplay pedals which are great because you can clip onto it from either side without any problems...  My shoes are adidas cause I happen to get a discount with them... But I am looking at the Specialized Trivent ones.

I would definitely get them!!

I was in your situation about 3 weeks ago. I ended up buying a pair of shimano carbon soled shoes (forget the exact model) and ultegra pedals. The difference was very noticeable, and I don't know why I had waited so long to switch.  You have plenty of time to get used to the shoe/clipless pedals. Make the switch you will be happy you did.

I've been riding clipless for about two weeks and I feel pretty comfortable, so I would say you definitely have time.  I did notice a small increase in speed and efficiency the first time I used them.  The biggest improvement was on the hills.

Can't really help you with brands.  I got a pair of used Look A3.1 pedals on craigslist for $20 and they definitely work for a beginner.

I just got my new road bike with the clipless pedals and shoes 1 week before my race. And was only able to ride twice before the race.  It went fine.  Just unclip your shoes while still rolling several meters before the stop. 
As far as better power, I can't say because I never had a road bike without them.  But since I just droped $300 for the pair lets say it makes a big difference

Thanks!  I'll be headed out for bike shoes sometime this week!