Grammatically speaking, all the three constructs are correct. The non-contracted first one is more formal. The choice between the other two can be made only by euphonic considerations, i.e. whichever sounds nicer or is easier to pronounce given the surrounding words.
The very colloquial I'd've is not unheard of either.
Answer from Armen Ծիրունյան on Stack ExchangeVideos
I would must be followed by an infinitive without to ( or perfect infinitive as in I would have gone). I had must be followed either by an object (a noun phrase, e.g. I had a little lamb, in which meaning it is rarely contracted) or by a verb's past participle. So it's (almost) always possible to distinguish between them by analyzing the words that follow.
Examples:
I'd go. (go = infinitive => 'd = would)
I'd had. (had = participle => 'd = had)
The only ambiguous case is when the verb's infinitive coincides with its participle.
I'd put. (could be would or had)
But these cases are rare and the meaning can be deduced if more context is provided
It will usually be clear from the context. For example, in the sentence I’d like to have a million dollars, I’d can only be a contraction of I would. By contrast, in I’d been there some time, it can only be a contraction of I had.
I only know ONE person, that uses the contraction “I’ld”, and she believes that this is an okay form to use. I really want to prove my friend wrong.