Wizards creates sets in blocks that are designed to work together. Recent blocks have two sets, and most older ones have three sets each. The blocks are designed as draft formats, and even the order in which packs of each set are drafted is part of the design. That way, the strengths and strategies in place after each pack can influence your ongoing picks, and knowledge of what is likely to be in the later packs can inform your early selections.
There are still unopened boosters from most of the 75+ sets in Magic’s history. This might not be true for much longer! Many of them are rather expensive, some are cheap. If you can source packs from the past, I suggest that you try some of the formats that Wizards designed, such as Journey Into Nyx / Born of the Gods / Theros, or triple-Khans of Tarkir. Some of the most beloved were Innistrad and Zendikar.
If you want to supplant some synergies with others, you can mix sets from various blocks. Some of my favorite sets are Journey Into Nyx, Fate Reforged, and Eldritch Moon. I think they each reward good planning. Mingling things like that, you might experience more random results, or you might stumble upon an incredible format. After all, the variance of a format, which basically means the importance of chance, is a factor that helps newer player sometimes beat experts.
A chaos draft is when each player brings packs from any three sets they can get their hands on. They begin by "drafting" which packs each drafter gets to open.
All you really need to have an 8-person draft is 360 cards. Many players take it upon themselves to design their own draft format by selecting individual cards for this purpose; this is known as a cube.
Cube is one of the contexts where proxies (counterfeit cards) are generally acceptable to use. Some cubes include proxies of the “power nine”, as well as other cards that are prohibitively expensive. Others closely mirror released formats, and include multiple copies of each common and uncommon. A cube gives you the chance to design a unique draft format, or build one designed by someone else, and then use it with your friends.