When to make suggestions that include cards in my own hand in clue?
You should almost always make suggestions that include one or two cards in your hand, especially after you know one or two of the real murder components. (Though this might change with the number of players. I'm used to playing with 3 or 4 people.)

The end goal isn't to know who holds which cards, it's to know which cards are not held. The most efficient way to gather information isn't when someone shows you a card, it's when they pass; especially when all other players pass. This does give information to other players, but more to you.

Illustrative Example

Let's say the real solution is Prof. Plum with the Rope in the Conservatory. It's Player A's turn and he's in the Conservatory. If Player A makes a random guess of cards he doesn't hold, maybe Player A gets lucky and accuses Prof. Plum (correct) with the Revolver, and of course the Conservatory. What Player A learns is who holds the Revolver. If he's extra lucky, the person holding the Revolver isn't  the person on his left, so maybe A will see a pass or two before being shown the Revolver, learning a more. However, if A suggests Ms. White (in hand) with the Knife (in hand) in the Conservatory, everyone will pass, and Player A learns that the Conservatory is the room! The other players will know that Player A made a big discovery---they desperately need to check out Ms. White and the Knife and the Conservatory, because at least one of those is part of the solution. But they don't know which one. (Ignoring the unlikely possibility of a wasted turn gamble where Player A deliberately made an accusation while holding all three cards.)

Now, let's step into another player's shoes. Player B knows that Player A learned something big, so she runs to the nearby Billiard Room and suggests Ms. White with the Knife. If anyone shows her a card, Player A knows that it's the Billiard Room, because he holds Ms. White and the Knife. Great! Player A learned as much as Player B did on Player B's turn. If people pass until Player A, he shows her, say, the Knife, and Player A knows that either Player B or someone sitting to his left before B holds the Billiard Room. Player A will now preferentially show the Knife rather than Ms. White to anyone. Meanwhile Player C can guess that Player A has one of the Knife or Ms. White, but Player C still has to make their own suggestion to find out which. 

Contrast this with Player B being a little more conniving: she decides to test Player A's knowledge more gradually. She accuses Col. Mustard (in her hand) with the Knife in the Billiard Room. Now if someone before Player A shows her a card, Player A can't be sure if it's the Billiard room or if it's Col. Mustard. If it gets around to Player A, he doesn't have a choice of what to show Player B, he must show the Knife, which is also better for B than if A gets to choose. So it's in Player B's best interest to make suggestions including cards from her hand too.

Other considerations

Suggesting 3 cards from your hand is a devious way to throw people off track, but you lose a turn of information gathering to do it. In my experience, the opportunity cost is too high for this to be worthwhile. 

Your card distribution (especially what rooms you hold) can affect your ability to make suggestions involving cards from your hand. I try to make one of the first 3 rooms I visit a room I hold. It's especially nice if you hold two secret passage rooms to hop back and forth between the two (though pretty soon everyone will know what you're doing). It can be tough if you hold only one card (or worse, none!) of a category. I'll focus on that category first so that I can at least alternately suggest 2 items when I get to the other categories.

It does make sense to not be too consistent. If you always make suggestions that include 2 cards from your hand, your opponents will learn this habit. Then the player who shows you a a card can be reasonably certain you hold the other two. Vary your play to keep your opponents from being too sure.

In the beginning of the game, it's fine to make suggestions with only one card you hold, or the occasional 0-held-card suggestion. You'll stil learn something--maybe you'll get lucky and learn a lot. But as soon as you know one category there's no point in making a suggestion involving a card in that category that someone else holds. You already know somebody holds the card, but you shouldn't care who.

tl;dr: You learn more from people passing than showing your cards. People pass more often if you make suggestions that use some cards from your hand.