Don't ride without one
There is no excuse for riding in anything other than a protective jacket designed for motorcycle use. You can find them at good local shops, and at hundreds of sites on the internet. To enhance the protective properties of your jacket, make sure the sleeves have zippers or velcro, so they snug up and won't slide up your arms in case of a crash. Look for good armor; CE-approved (European Union standard) is better than plain foam or EVA. The jacket should zip to your riding pants, either via a zipper in the back or a 360 degree one. Many manufacturers will provide an extra half zipper that you can sew to the pants, if the zippers on the jacket and pants don't match.
Leather vs Cordura (often called "Textile")
It's difficult to say which is "better". Leather offers better abrasion resistance and sustains damage better in a getoff; it is also generally heavier, more difficult to care for, and not as versatile. Cordura (a high-denier nylon blend) breathes better, is waterproof, doesn't look as 'super hero' like, and is generally more lightweight and comfortable.
The best cordura suits, like Leon's Aerostich
are certainly better than a cheap leather ensemble. Cordura clothing can be just as well padded as leather, and carry the same armor.
Another fabric alternative is mesh. While some long-term riders haven't accepted it, it is a cooler alternative if you often ride in hot, humid weather. Its abrasion resistance is probably not as good as regular textile. If you're looking at mesh gear, try to find some that has leather or textile inserts at critical impact areas, such as the elbows and shoulders. Make sure it also has good armor.
Product reviews and comparisons at MotorcycleCruiser.com