Even in quick speech, there would be no contractions. While 'would' is often contracted to 'd' in speech, it isn't contracted when it's in initial position in a question, so you'd pronounce the full form of the word 'would' here. Unusually, there are no schwas in this sentence, either. In mid-position, 'for' would normally be weakened to /fə(r)/, but here it comes at the end of the question, so it needs its full form. The only weakened syllable would be the auxiliary 'be', which might be reduced to a short 'bih' sound instead of the full 'bee'. The 'I' might also be shortened, unless you're emphasising it ( as in "What would I be looking for? as opposed to "What would you be looking for?") Personally, I'd say it something like this, with the primary stress on the 'look': /wɒʔ wʊda bɪ lʊkɪŋ fɔː/ Note the ʔ, which is a glottal stop where the 't' is kind of swallowed, and the way that the word 'I' (when not emphasised) follows straight on from the 'would'. Of course, there are many different native-speaker accents, so other English speakers would say this in different ways.

"a summary" is possibly the word you're looking for ?? That's when you give the main points of a discussion, but without giving all the details. For example, if I read a book, I could give you the main points or summary in just a few minutes. Or, you speak for 30 minutes and I give someone the summary of what you said. That is, in a few minutes I talk about what you said. Otherwise, a 'quick speech' is just a short speech - you are talking for only a short period of time. A short presentation is the same - you are talking on a topic but only for a short period of time.

What do you mean "a quick speech"? Do you mean is there a simpler way of saying this? I might simplify it to What am I looking for?