One more bike type to consider: Look at a touring bike. It has a frame that resembles a road bike, with the dropped handlebars, but is designed more for comfort, slightly more upright, than a road bike. Like a cyclocross bike, it can handle more surfaces than the road bike, though.
If you've read through other posts here about bike types, you'll see there are a few of us here who are not fans of hybrids. My feeling (and I won't speak for anyone else) is that hybrids end up losing the best features of the road bike *and* the mountain bike. You end up with a generic bike that doesn't handle as well on paved surfaces or trails. My vote is usually for a cyclocross or touring bike for the first bike. Unless you plan to mostly mountain bike, in which case go for that!
About the seat, you want to make sure that it's made for women & not for men. At least I assume, from your name, that you're a woman. This is important as they're made differently for certain anatomical differences. This can go a long way to prevent problems & keep from tiring as quickly if you have the right saddle.
I agree with Jim that you probably don't want a road bike (curved handlebars). You can't (or shouldn't) ride a road bike on dirt. You can, however, ride mountain, cyclocross, and hybrid bikes on both pavement and dirt.
That being said, Jim has a good point with the cyclocross. If you can't find a cyclocross bike, however, you can go with either the mountain bike or the hybrid. If you want to change up the tires on either of those bikes, you can buy slicks. Slicks are tires with smoother tread, which allows the bike to move easier over pavement.
The hybrid bike will have you sitting up straighter, while the mountain and cyclocross bikes will have you more bent over. Sitting up is more comfortable, but being in a slightly bent position is more aerodynamic and will make it easier to pedal into the wind. Which for me, seems to be pretty much any direction I want go!
The bike sales person should spend some time with you answering your questions. If they try to rush you, say thanks for your time and go somewhere else.
"God gave you your body as a gift, so you should take care of it." - My Mom
Here are some answers to your questions although general others will pipe in with specifics:
1 Handle bars: try both and see what is more comfortable to you. It sounds like you will lean towards the straight (mountain) vs drops (racing)
2. Some would recommend a hybrid but I would steer you to a cyclo-cross frame. If you ever go to just strictly road riding all you would have to do is switch out your tires for much skinnier ones.
3. Get whatever seat (saddle) is comfortable but I would recommend to stay away from gel. If you are measured properly and fitted properly and with a nice pair of padded cycling shorts you should not need a gel seat (saddle).
4. See my comment on on 2 but I would recommend a cyclo-cross frame.
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