Quotations are safe to use during public speaking engagements because if the quotation is not funny, it doesn't matter since you are just reciting it. You did not write it. It can still be used to make your point.
You can use the power of the name of the person who did write it. People will be more likely to laugh or at least chuckle if a famous person made up the quotation.
If you are not sure to whom the quotation belongs, it does not matter at all. Unless I am absolutely certain who said something, I always give myself an out. I usually say 'I BELIEVE' it was ____________ who said. This keeps me out of trouble for attributing the quotation to the wrong person. Sometimes I say, 'My great, great grandpappy used to say . . .;, or 'My old aunt Maude used to say . . . ;. However, if you know for sure who said something and their name carries weight, go ahead and use it.
There are literally thousands and thousands of notable quotations available to you. Stop at any bookstore and look at quotation books. You can also look on the Internet for searchable quotation web sites. Here are just a few examples of some of my favorite quotations:
Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing had happened. Winston Churchill I am a friend of the workingman, and I would rather be his friend than be one. Clarence Darrow I never made a mistake in my life; at least, never one that I couldn't explain away afterward. Rudyard Kipling Get your facts first and then you can distort them as much as you please. Mark Twain Many of us spend half our time wishing for things we could have if we didn't spend half our time wishing. Alexander Woollcott He is more apt to contribute heat than light to a discussion. Woodrow Wilson Everything comes to him who hustles while he waits. Thomas Edison When you have got an elephant by the hind legs and he is trying to run away, it's best to let him run. Abe Lincoln It takes less time to do a thing right than to explain why you did it wrong. Henry Wadsworth Longfellow When you get to the end of your rope, tie a knot and hang on. Franklin Delano Roosevelt In the first place God made idiots; this was for practice. Then he made school boards. Mark Twain
(take out school boards and substitute anything that fits your purpose).
When you are being funny, don't feel bad about twisting the quotations to meet your situation. Mark Twain will never say a word about it. Neither will anyone else if you introduce your quotation by saying, 'Someone once said,' or 'My great, great, grandpappy used to say.' Then change the quotation around any way that suits you.