What is the most important component?
 

On a good bike it's the frame.
On a hybrid I don't think it matters.

Enjoy

The most important component is the rider. After that, it depends on what you want the bike to do. Looking for performance/light weight? The frame is key. Comfort? Then the saddle becomes important. Capability on widely varying terrain? Then the gears are important.

For reviews, try http://www.roadbikereview.com.

I am planning to ride mostly on pavement or beaten trails, I'd like to do some distance (usually under 75KM/50 miles at one go), nothing serious at the moment. I have been looking at Trek 7200/7300, Devinci St.Tropez/Stockholm, Giant Cypress LX/DX.

Besides the frame, the bearing components are important. Most people prioritise the hubs, but in my experience, the bottom bracket has a tougher life. A decent UN52 catridge BB is worthwhile on any low-end utility bike.
For wheels, the quality of the build is just as important as the components. My Altus hubs are into their 4th year of trouble-free commuting, in a hand-built wheel.

Are there any disadvantages to anti-puncture tires?

GOod frame will suit its intended purpose. A good DH frame will be welded nicely, not made from these ultra light alloys, big travel and well designed. AN XC frame wont be made of lead with 8" of travel. Look at material used. Another thing on a good bike which is significant is wheels

For a hybrid I would honestly say the tires are the most important.

My list of priorities on a bike...

1. Frame
2. Wheels (includes hubs, spokes, rims)
3. Fork (includes headset)
4. Drivetrain components (includes shifters, gears, derailleurs, cranks, BB)
5. Other components (saddle, stem, handlebar, grips, pedals, etc...)

I based this list on what's the least easily and economically feasable to change/replace... in other words, what you're locked into when buying the bike.

I agree except I'd slot the contact points-saddle/pedals etc into 2nd spot.

Well, my criteria was ease/cost of change. I tend to think that things like saddle and pedals are easier and cheaper to change than wheels and forks. I'm not as locked into a saddle or pedal as much as I am with the other parts. Most bikeshops will swap saddles and pedals on the spot. Thus I list those other components higher on the descrimination scale. Think about it this way: Given two bikes where bike A has a saddle you don't like and bike B has wheels that you don't like but everything else between them is the same. Which bike would be the easiest to get to a situation where you'd accept the bike?

They're heavier. And sometimes they don't always work well.

As pointed out - weight. But that doesn't mean they aren't a good choice anyway. Some work better than others, but the hard part is getting useful info from others. You can go to roadbikereview.com and look at lots of reviews - some tires have lots of them, others have none.

But the comments can be downright silly to minimally useful. For example, someone gets a flat resistant tire and complains because it isn't "bullet-proof". Well, no tire is bullet-proof. Even steel belted car tires get flats!

Or they get a flat in a short time. Well, all tires get flats. A given tire in your riding conditions might average one flat every 1000 miles - but you might get that flat in the first 10 miles. Doesn't make it a bad tire. Just bad timing.

Or people tell you they only got one flat a week (or month, etc) on some tire. So what? Some people ride a lot in a week. Others don't ride much at all. Mileage is what you need to know.

I've used a number of tires having various resistance. My Carbon Comps that came on my newest bike would start out okay each time I replaced them, but the rubber was soft, resulting in lots of cuts. I found that a cut on these tires (minimal protection) tended to keep causing flats, but they were fast tires.

I used one Continental GP3000 on the rear (where most flats occur) and got about 2600 miles before the first flat. But one tire is not much to base things on.

I presently have Contiental 4 season tires front and back and am over 500 miles with no flat so far. But I also used them on my prior bike and found that they did fine for around 700 miles and then started getting a lot of flats. However, my roads are much clearer now than they used to be (construction is done).

I used Armadillos on my old bike some and they had the best record, though with all the construction at the time, they still got their share of flats. They are heavy. The GP3000 is 10 grams heavier than the Carbon Comps and the 4 seasons are 10 grams heavier than that. Don't recall the weight of the Armadillos, but they are quite a bit heavier.

Remember, weight may slow you down slightly, but a flat slows you down a LOT.

Thank you everyone for your posts, they are greatly appreciated. Would love to see more!