And now for a differing opinion.
I don't ever pay in cash (unless they don't accept credit cards). I only use cc's. There is no reason to worry about credit card fraud as long as you check your cc bill each month when it arrives. If abuse occurs and you notify your cc company you have zero liability. If you use your cc to pay you have recourse if something goes wrong. You can dispute the charge and get your money back. Try that after having paid with cash and you'll get nowhere. Also, if you use your cc it will reduce the amount of cash you need to carry and / or withdrawal from the ATM.
The best way to book depends upon your travel style, where you are and when. If you're traveling to a popular destination during peak season you'll need to make advance reservations, typically over the Internet. If you prefer not to plan things out to much and you're able to wait until you arrive, it allows you to preview the property and your room to make sure it's satisfactory. Also, if they are hurting for business you can generally bargain more effectively as a walk-in who could easily turn around and walk out.
Of course, these are just generalities and specific situations may differ.
Good luck.