Have you tried a plunger, yet? It will clear most toilet clogs and is easier to use than a snake. Flush three or more times afterward to help ensure the drain is cleared.
If it's a more stubborn clog, a toilet auger should be used. It's a 6' snake in a piece of tubing that is curved at the end and jacketed to help keep the porcelain from getting scratched.

Yes, the plunger is useless.

The $60.00 closet auger is probably along the lines of the ones I use, make by Ridgid/Kollman and available at Home Depot. Like many tools, if you buy the cheap one it might work, but could be frustrating in its operation, cheap and flimsy feeling and just barely able to do the job, and after you can't get that one to work you may end up going and buying the expensive one anyway. If its something you think you may use often, you might want to get the expensive one.
If your toilets are those 1.6 gallon watersaver type then a good closet auger is standard equipment in your home. These toilets have been nothing but a pain in the butt (pardon the pun) for us plumbers since they have been required by code starting in 1993.--The Captain

We finally bought an auger at HD because DH got tired of renting one all the time. Easy to use and works well. It was under $50 and is well worth it. A plumber I just interviewed for our new kitchen and masterbath said he recommends people buy them for wedding and housewarming presents! ha!

Plunger is worthless at my house also.

Do any of you find a difference in brands of toilet paper and clogging? I know I had a problem once when I bought Charmin and later heard a few more say the same thing so no more Charmin for me.

I am a Kindergarten teacher with 21 children and one bathroom. Lets just say....I am a living expert on clogs. And, guess what? I know the secret. Dawn. Yes, the dish detergent. It is my secret weapon. Just put a ring around and let it go down. It also keeps them free running. I cannot remember the last time I had to resort to a plunger. Plus, who wants to do all that while wearing business attire?
Come to think of it, who ever wants to use a plunger?

Most toilet 'clogs' are in the trap built into the bowl and easily cleared with a plunger.
The plunger needs to be used correctly though.

You want to force water (NOT air) into the drain opening from the bowl.

If you are having repeated clogs AFTER the bowl trap something is very wrong.

The line from the toilet is at least 3 inches in diameter (with 4 inches being very common) and the trap is smaller than that.

Plunging in a business suit should not be a problem.
You are not going to spray water around unless you are doing it wrong (badly wrong).