Learn English – Usage of “make” and “become”

I’d like X expresses a desire or preference for X, and ordinarily everything else necessary for your hearer to understand what you mean can be inferred from context. “Have” is just fluff: presumably you don’t want to “have” some typing paper, you want to type on it. If you tell your office manager “I’d like some typing paper”, she will understand that you want her to give you some typing paper, and if you say the same thing to a sales clerk at Office Max, she will understand that you are ready to purchase some typing paper.

This not to imply that you should be careful to omit the to have—it may be unnecessary, but it doesn’t do any harm.

Note, however, that if you employ a verb with like, it must be a marked infinitive:

I’d like to see how it functions.
I’d like you to get hold of Bob and see what he thinks. (In this case the marker distributes over both infinitives)

Your other example is a little more complicated. What you want is a defined goal (the participle is postposited because it bears a postposited adjunct). This may be expressed a number of ways:

I’d like to have a goal defined before we begin.
I'd like to get a goal defined before we begin.
I’d like a goal to be defined before we begin.
I’d like us to define a goal before we begin.

They all amount to pretty much the same thing, and are equivalent to “I’d like a goal defined before we begin.”

"Hi, Travis . I love these piggies," I'd gushed, straining to touch one.

Is effectively the same as:

"Hi, Travis . I love these piggies," I'd gushed while straining to touch one.

To convey some kind of sequence, you can make it explicit...

"Hi, Travis . I love these piggies," I'd gushed before straining to touch one.

...or by simply shifting both into the same tense:

"Hi, Travis . I love these piggies," I'd gushed and strained to touch one.

"Hi, Travis . I love these piggies," I'd gushed, then strained to touch one.