Top three things...

1. Fit
2. Fit
3. Fit

Then, make sure it's a good fit.

After that,

1. Set a budget. This, more likely than not, will dictate your choices and limit your search.
2. Educate yourself on frame materials, component levels, and what each brand has to offer. 95% of this you can determine online.
3. Shop until you drop. Visit as many local bike shops as feasible, expand your search as wide as you're willing to travel for purchase and service. How the dealer treats you when you're shopping will tell a lot about how they will treat you when you go in for service.

Finally, by all means post your specific questions here. There are a lot of knowledgeable folks here who are more than willing to show you how much they know.

Fit is the end all be all important thing.  You could buy a $3000 bike, but if it does not fit well, you are wasting your money.

Cost if course is a factor, and for me, I have to like the way it looks (That might just be a girl thing though)

Agree - the most important - don't look at the name - go for the fit - if you are riding 56 miles in a HIM - you want comfort 

Well, you're hopefully going to end up not just purchasing a bike, but also establishing a relationship with the shop. Yes, you can buy stuff online but for repairs, adjustments, advice, and those 'gotta have it now' purchases you'll be going to the LBS. And they're not all the same, particularly when it comes to people who want to ride in triathlons.

So before you go shopping for a bike, I recommend that you go shopping for a bike shop.  Try this: Go to 3 different shops around the same time, and see how the staff is. Explain what you're looking for, ask questions, look around. See if you get pressured to buy what they have right there on the floor or if they find out what would be best for you first. Let them know that you're just starting out with this kind of cycling and see how they react.

Also, ask around about experiences that other people have had in local shops. Ask who are the best people to deal with.

You will get a test ride, but probably only for a few minutes.  My LBS will rent you a bike and let you take it out for a longer ride.  Then they apply the price of the rent to the purchase price if you buy it.  You should be able to tell if a bike is a good fit or not with a 10 min test ride.  Long term comfort is more a matter of proper adjustment and replacing the saddle.  Both of my bikes were bought with a budget in mind that included spending money on a saddle after the bike purchase.  Both stock saddles were replaced before the first ride.  There are some women specific saddles out there you should take a look at if you're going to do a HIM.

Those are kinda sorta some red herrings that Jorge has thrown out there. Simplified:

• If you're set on a road bike (as you indicated), then geometry is a non-factor. But here's a good article on tri versus road bikes.
• Unless your budget is, say, >$1500, you don't have to worry about carbon; ~$2,500 for titanium.
• For the most part, your budget will also determine your component level. Get the highest level you can afford.

As I said previously, do your research and educate yourself!

OP - it might sound intimidating but really it is very simple; do some research and you'll learn a lot about bikes, geometry, components, etc.

check out bike websites such as trek, giant, felt, cannondale, cervelo, etc.

Just a quick clarification for you...everyone mentions "components."  What they are mainly referring to is the shifting system on the bike.  "Most" bikes will come with SHIMANO brand shifting systems.  Shimano order of quality (light weight, smooth operation, etc.) is

Sora (lower end)

Tiagra

105

Ultegra

Dura Ace (best)

Look at the rear derailer system and it's labeled right on there what it is.  If it works with your budget and fit requirements, I'd attempt to get a bike with a minimun of 105 components.

To start - I will admit that I am somewhat of a spreadsheet geek when it comes to making large purchases.  I am preparing to buy a new bike and this is what I have done. 

1.  I created a spread sheet that has columns for Manufacturer, Model, Drivetrain (components), wheels, crankset, weight and price.  I looked up all kinds of bikes from several makers and copied the info into the table.

2.  Now - I can sort the table in any form that I want, such as by price and then component and then weight.  I can decide what is the most important to me and set the table up to give me my top 5 or whatever.

3.  Now - I go out to the LBS that has these bikes and I try them out, ride them and see how they fit.  Which one do I like better.  Which one seems more comfortable.  From that I can make a decision, stay within my budget, and put greater emphasis on what is most important to me while keeping it all straight in my head.

Look at the brake/shift levers, they'll show the "grade" component too, and are the more expensive part of the setup.  Rear deraileur's are $40-150 as you move up the line.  Integrated shifter/brake levers are $120-500.  You might be willing to upgrade the rear deraileur (Not always advisable/compatible) well before you upgrade shifters. 

After fit

remember that there are bags/bottles/cages/pedals/inflator/tools/etc. that'll add to the cost of the bike.  Most mid-line bikes don't come with pedals, so you could swap pedals from your hybrid, but more likely will buy another set for your new love. 

A good bike shop ought to let you take a fairly long test ride (possibly on a trainer in their store), so go dressed and prepared to ride 30+ minutes.  The shop should include some bike fit work for you (more comprehensive as you go up in price).  The fit might involve 30 minutes of riding too. 

i'd just look for the coolest color scheme.....      

(cool bike.jpg)

Quite honestly, if you're  looking for under $1000, you may want to go with a road bike and put on aerobars.  That's going to be your most versatile investment.  You can take the Aero bars off for the winter and have them on for Tri season.

Keep in mind that the fit will be different for each set up (Tri vs. Road).

A way to get a great test ride is to ask the shop if they have a weekly shop ride.  If they do, ask if you can test the bike out on the ride.  I know at my old shop, they would let you ride the bike and it gives you a chance to really test it out.  Can't hurt to ask.

And in regards to clipless pedals... YES YES YES.