You hear this question from new(ish) players every once in a while: Why is Preordain banned in Modern, but not Serum Visions? Sure, they are close, but they are not the same. That ordering changes the card quite a bit. Also, they have to draw the line somewhere. [Note: Preordain has since been unbanned in Modern.]
This is an interaction that comes up every once in a while. For example, currently, this combination of cards is being played:
When to Scry First
Simply put: when you need something specific right now.
Suppose you have your Tenth District Legionnaire out and it’s going to win you the game, except that your opponent decides to use their Cast Down. Now, you know you have a Gods Willing in your deck and you need it right now, so you play your Samut's Sprint to draw a card through Season of Growth
In this case, you want to see as many cards as possible. So, if you draw first and scry after that, you get to see two cards, but the second one will remain in your library. If you do it the other way around you, you get two chances to draw that card right then and there.
Same thing with various Storm-style decks which want to cast many cards in the same round. You want to see as many cards as possible, so you want to scry first.
When to Draw First
When you scry, it’s a good idea to have as much information as possible. So, if you aren’t looking for anything specific, drawing first might be a good idea, because that gives you one more data point.
This is where knowing your deck helps. Are you able to and do you want to use mana for the rest of your turn? If not, than you should probably draw first. You will still see as many cards, but when you make your scry decision, you’ll have more information to base your scry on.
What If You Have More Than One Scry or Draw?
Mostly, just follow the rules from before. If you really need something right now, scry first, if you want the information for the scrying, draw first.
Of course, it’s not always quite this simple. Suppose you want to make a play before your next turn and have two draws and a scry. What do you do? Draw, scry, draw. Why? This plays both sides. You see as many cards as possible, but at the same time you also gain extra information.
Now, if you have two scries and a draw, you might have to think a bit on this. If you need something specific, do both scries first, but if this isn’t your goal, you can maximize the value of the scries by keeping them apart with the draw. Why? Because you if you want to keep the first card on top, the second scry would be wasted.
Same goes in a situation with several of both. Keep the scrying interspersed to maximize the value of each.