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7 out of how many people? He offered so that takes most of the pressure off of you to just ask for what you want, but you're right, it's not an all-you-can-eat buffet. It's like when you're a kid and your friend's parent tells you to pick what you want from the store and you come back with a shopping cart loaded with the whole candy aisle when they just meant to grab a candy bar or a bag of chips.

It shows that your contact thinks highly enough of you to risk his reputation by giving you access to their network, so that says a lot. People are protective of their networks so I wouldn't be careless with their respect. I'd pick the 3 people you want to speak with the most if it was me. It's better to ask for less and be offered more than ask for more and risk making an ass out of yourself. But asking for too little can signal shyness and insecurity which isn't always good either...

Pick 3 people and have a good reason or story for why you want to be introduced to them. Tell your contact what you hope to get out of the introduction, and it will also allow your contact to guide you toward someone who may be a better fit for what you want/need. Who knows, someone who you overlooked may be the one you should speak with and the one you wanted to speak with wouldn't be a good fit. Give your contact something to work with.