Modern bars should fit, you might have to bend the stem out a tiny bit (<1mm), but nothing thats un-doable.
700C tires WILL NOT fit 27" wheels. I think tubes can be interchangable, but I'm not sure, thats just going off of the fact that the tubes I use have some crap written on the box about 27" as well as all the stuff I really pay attention to that says 700C 18/23.
I suggest getting your wheel from Tony at IRO instead of eBay. Chances are you'll be happier for the same money.
I'd be careful using the stock cranks and going down to 700C. My 70's Raleigh Grand Prix with 165mm cranks (I think the old cottered cranks were closer to 170's) and 700C wheels has some serious pedal clearance problems due to it's low BB height. Pedal strike on a fixie is not fun! Also, if your cranks are cottered, make sure you run a brake!!!!
i just got some basic wheels(silver aeroheads) from IRO and they're quite nice looking. under 200 for both wheels, i think the rear is about 100$. i got fixed/fixed and they came(per request) spaced for 126mm. great deal.
If you're only getting one wheel, get the 27" fixed from Harris. A 700C rear + 27" front will may the geometry slacker than it already is. Or you can go 700C on both but if the brake's not a standard ("long") reach caliper, you'll need to get one. Also, it'll lower your bottom bracket as mentioned.
I agree with the other guys about not "necessarily" going the ebay route. That being said, you may find a good track wheel there. IRO is great for cheaply priced stuff (decent quality).
My personal opinion is that when you're building / buying a fixed gear bike, the biggest place to take your time and get something of a higher quality is the rear wheel. On my first few fixies, the rear wheel was significantly higher quality than any of my other components.
If you're anything like most people here on the boards, then this will not be your last fixie...or you at least won't stop at this build (upgrades etc). So another way to think about it, is that if you get a good rear wheel (good hub, good rim) then it will last you forever (well the rim may not last a long time).
As for the 27" wheel. If you're on a budget...ebay or the basement of your LBS could be a jackpot here. All you need is ANY trued road wheel (700c). You can always get a matching wheelset front and back...but the most important thing is to get you on the road...so I would just get ANY 700C road wheel...
Thanks for the input... I decided to go with IRO since they are local to me. I can pick up the wheelset save shipping and support a decent local shop. I'll try and get away with the cranks that are on there for the time being. I'll mostly be training on this so it won't be a primary mode of transport. However I'll probably upgrade eventually.