I don't paint much but my sister does, and according to her, oil paint is a lot fussier and harder to work with than acrylic. Oil takes a little more patience to use, and acrylic (which I've used before) is simpler- it's the kind they market as kiddie paint.
As for consistency, oil is on the thick side, and sort of sticky, while acrylic is more watery and slick. Both types yield similar, but definitely not identical results so I think you should probably give both a try see which you not only prefer working with, but prefer the look of. Perhaps you'll like both!
Oil paint dries slowly and mixes well on canvas (A thin paint will stick to a thick paint). It also adds texture but shows brush strokes. You are going to want to work in a ventilated area.
Acrylic dries very quickly and dries flat, diminishing brush stroke visibility. Once dried it remains flexible and can be painted over quite easily. When wet it is soluble to water but becomes insoluble once dried.
I recommend acrylic as an introduction as it is easier to work with and is more forgiving. Another solution would be to start with water colors like gouache or aquarelle. These mediums are easier to clean and more portable, but can't be painted over like you can do with acrylic.
I'll have to agree with the others that acrylic is much easier to use. I've done mostly watercolor and acrylic on all my pieces, and have figured out the basic rules to get the best results. But oil, the few times I've dabbled with it, has proved to be a little more difficult. It also requires more than just water to dip it in and clean it off. In fact, you don't use water at all (except for the end process of cleaning) – you have to get oils and turpentine.
Acrylic is easier to start with, yes, absolutely. But unless you're allergic to turpentine I would actually say you should figure out which painters you like and what styles you want to emulate, and decide based on that.
Let's say you're way into Rococo paintings. In that case, getting the look right would actually be a lot harder if you're using acrylics. Not only will the layered colors not look quite right, but the quick drying time of acrylics will make it very difficult to paint in this style.
Consider too that there is a lot to learn about mediums in acrylics. You can use just water and paints, but you're going to have a better experience if you also at least have some retarder and GAC. I like to use self-leveling gel, and most acrylic painters agree it's good to have a selection of gloss and matt acrylic mediums in a variety of consistencies.
Water mixable oil paints do exist, and they do get recommended for beginning oil painters. I do /not/ recommend them for learning, because it keeps you from learning about the oil mediums.
Allow me to suggest an alternative,
Next visit to the Arts & Crafts Store, look for water color pencils. This is a relatively new medium that experienced and novice artists can incorporate into their personal pantheon of skills.
These pencils allow the artist to sharpen washes and generally enhance works nearing completion without introducing a polluted color. They look like colored pencils and act like colored pencils until water is stroked across them, at which point the melt and have the attributes of water colors.
Generally speaking, acrylic is a cheaper and more forgiving medium to start with. As mentioned by other respondents, acrylic is fast-drying and can be painted over. You can also use acrylic media, such as glosses, gels, pastes, etc., to adjust the consistency and texture of acrylic paint. I personally use acrylic paste and gels to thicken the paint such that it can be textured like oil paint. You can also use acrylic paint like watercolors by diluting with water if you are painting on a porous surface (like paper). If you're new to painting and haven't decided on a style yet, acrylic paint is a great paint to begin experimenting with because of how versatile it is.
Acrylic is also easier to start with because it doesn't require as much specialized material. Before drying, the paint is water-soluble, so you can clean brushes with water and mild soap. (But make sure you wash your brushes before the paint dries! Once acrylic paint dries, it forms a polymer finish, which is insoluble in water. This also means acrylic paints can work as fabric paint as well. ;]) But with oil paint, you need turpentine for cleaning brushes. And of course, oil for the paint. You also need to learn a proper order for applying paints ("fat over lean") in order for the colors to show up properly in the end product.