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Have you used oils on anything but a canvas? The ideal surface for oils is canvas, yet primed/gessoed illustration boards and linen work fine, too. Important thing about using oils, as with acrylic, is they only paint on gessoed surfaces; otherwise, the paints seep through, sodden, and scrape off cloth, cardboard, and masonite, respectively. I think bristol paper or hot/cold press 140+ lb watercolor paper always is an option for all painting mediums. Regardless, there are a few mediums to paint with:
Oil
Acrylic
Gouache
Watercolor
Ink
Computer
Oils are the traditional painting medium. Old masters have created memorable works with them. Benefit of using oils is that they smoothly blend colors, for they take a long time to dry. However, you need plenty patience to finish a painting with oils! It is a delicate medium as mixing too quickly or too much color will dull and mud the colors. It is often the most expensive, particularly for you need to buy gamsol, sturdy brushes like bristle-haired to hold the oil-based paint, and it is crucial after every painting session to throughly wash your brushes. This medium needs the most care. I think it befriends you best if you have the time.
Acrylics work very much like oils, except they dry faster than half the time oils will! They're water based, so you do not need to buy gamsol. There are many "acrylic mediums", like glazing/gloss mediums, slow-dry/retarder gels, and textured paste meant only for use with acrylics, which able you to achieve various and playful surfaces. The benefit of acrylics drying so fast is also its downfall; very often the colors do not blend to your will. There are water-based oils, but I believe these are too segregated and expensive to work with you in the long run. You can easily vary the viscosity of acrylics, from water thin to straight out of the tube thickness, so in a way it is very sturdy. As well as for the next two kinds of paintings, always keep your brushes in water while you paint!
Gouache may improvise as acrylics, oils, and watercolor, because you can easily manipulate its viscosity. Most likely it is acrylic's twin. It dries faster than acrylics, however, and it is water-based, so I consider it as an illustrator's efficient tool. But, using it thickly, you may achieve brilliant colors as in oil painting, and, watered down, play with it like watercolors. It is cost-effective.
Watercolor, if used with ample water, blends like oil, but leaves washes. You are advised not to use this medium as thick as oils. Compared with the aforementioned mediums, watercolor leaves it own unique impression: your finished paintings end with a watery beauty. But it depends how bold you're willing to blend and add layers of colors. The process to make a somewhat professional watercolor piece is very delicate, as you need patience to let the paint dry and add shades of layers, and to achieve watercolor 100%, every stroke and layer added is final, so you must carefully obtain whites from the paper. There are also watercolor pencils, where you draw and add water, but it doesn't blend colors as magically as the watercolors. Even so, the greatest advantage of watercolor is that the dried pigment on you palette dish is reusable by just adding water!
Ink is also considered a "painting medium", if you use brush and water. I should mention "sumi painting" which is a Japanese style of applying ink on paper, where you play with your marks by simplifying the details from figures/still life. Primarily, your palette is black-white-gray, but there are colored inks, and even acrylic inks. You try this style much like you would with pen, and watercolor for the washes. Easiest medium.
For the modern era, computer and digital painting are another means of painting. I highly recommend using a tablet (such as wacom, et alia) than working your digital painting with a mouse. Depending on your program (i.e. SAI and Photoshop), you may easily apply the blending effect and painless experimentation of coloring without the smell or clean-up of real paints. But you're limited to the computer, and it is costly. If you're into animation and comic art, this is a consideration for the future.
If you're a beginner, I recommend acrylics. Gouache and watercolor if money is an issue. But I encourage you to try oils, too. Experimentation is the key to understanding your own relationship with any painting medium.