The phrase share of, particularly when preceeded by a pronoun, refers to some amount that is rightfully owed to someone, or expected for someone, like when a pirate talks about his share of the treasure, or a member of a team of bank robbers talks about his share of the cash. However, the expression is often used metaphorically to refer to some unspecified amount. For example, a manager of a failed project might talk about his share of the blame.
In this case, my share of women means that the character has been lucky in love. He hasn't just had two or three girlfriends, he's had several. And when he emphasizes that by humorously adding, "In fact, I've been with like a lot of people's share of women," he means that, whatever number someone's "share of women" would be, you could probably triple that, and that's how many women the character has been with. In other words, he's a self-described Casanova.
So, the expression "I've been with like a lot of people's share of women" is intended to be a humorous way of saying that he has been in a lot of relationships with women, probably mostly short-term relationships. Yet, in spite of all this "experience," he's never felt a lasting, close, affection like Ross has for Rachel.
I've never watched Friends, but I'm guessing that these lines are meant to be both funny and touching at the same time.
"Despair" sounds like "the spare." Alas
"I won't let a flat tire get me down," Tom said, without "the spare".
The definition of spare at Oxford includes
A spare tire
Note: at first I thought it was a pun on "without the air", but realised it was "without the spare."
Best Answer
"Never let it be said that ..." means "Don't let it be said that ..." means "Don't allow anyone to say that ..." So what it means is, if anyone ever says that this person doesn't collect the best, you should correct them. You should explain to them that, no, that's wrong, this person does collect the best. You shouldn't allow anyone to say that the person doesn't collect the best, without arguing with them. It should never go unnoticed, you should always try and make sure people don't get away with saying that.
That's what the expression means literally. In reality, it's usually used figuratively, just as an intensifier. So it really just means "I definitely collect the best" (and anyone who thinks otherwise is mistaken. So misguidedly mistaken that you should always correct them.) But the bit in brackets is not usually meant seriously. Usually, as I say, "never let it be said that xyz" means "xyz is very wrong".
So here, "never let it be said I don't collect the best" means "the idea that I don't collect the best is really wrong" means "I most definitely collect the best".