D&D5 - The bad guy should not be surprised.
PHB, p.189 - Surprise
A band of adventurers sneaks up on a bandit camp, springing from the trees to attack them. A gelatinous cube glides down a dungeon passage, unnoticed by the adventurers until the cube engulfs one of them. In these situations, one side of the battle gains surprise over the other.
The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn’t notice a threat is surprised at the start of the encounter.
As @KorvinStarmast stated, there is no such thing as a surprise round in 5E. A surprised character is simply not able to move, take an action or a reaction on his first turn of the combat.
In your situation, the bad guy is clearly facing the characters when doing his speech, so unless he is fanatically speaking to his hidden god of evil somewhere in the skies, he will see the character doing his move and won't be surprised.
If the party was speaking with a friendly noble NPC, for example, and a PC decided to attack suddenly, the NPC should be surprised, because he wasn't aware of the threat. When a BBEG faces a party of characters, it seems obvious that they are antagonists/foes/enemies and that each side is a threat to the other. In the end, it is the definition of threat that makes a difference.
Also, giving the player a round during which he alone can act might lead others to abuse this mechanic.
This is what the PHB says about scenarios that demonstrate one group surprising another:
A band of adventurers sneaks up on a bandit camp, springing from the trees to attack them. A gelatinous cube glides down a dungeon passage, unnoticed by the adventurers until the cube engulfs one of them. In these situations, one side of the battle gains surprise over the other.
So it's being shown to us that the encounter wherein creatures can be considered surprised begins when one group takes hostile action against the other group that has not noticed the first. And note that surprise can only happen when you are in the first round of the encounter, which means that, if you want to take advantage of surprise, Initiative cannot be rolled before the start of the ambush.
It also doesn't make sense to give someone the surprised status when nothing is surprising them (ie, the players are planning, not ambushing). When you are surprised, you cannot move. Does the act of the players planning somehow paralyze the other group? No, it shouldn't.
Best Answer
Theoretically every enemy has his own initiative roll. But this is often quite tedious and you can for example roll for every group of enemies. For example if you have four Goblins that are armed with a Shortbow and you have two Goblins armed with a Scimitar you could make six Initiative throws. But you could also just make one Throw for the group of melee Goblins and one Throw for the group of ranged Goblins.
This makes the Initiative phase faster and it also means that you can move all enemies at once, which is easier because you only have to assess the situation once when moving the enemies. But it can also be harder for your players as all the ranged Goblins are attacking at once. If they take aim at the same PC this could be quite hard. You could make them attack different targets though, depending on their tactic and your preferred approach.
To keep track of the initiative and the general battlefield from the player's perspective we use a Whiteboard where the players can mark their positions and the enemies positions. The Initiative order is defined with magnets, each of which has either a players name on it or a creature's type, like "Ranged Goblin".
Keeping track of the health is often done by noting the points on a sheet of paper. For example I like to make a very, very rough sketch of the terrain for myself on a DIN A4 sheet of paper behind my DM screen and mark each enemies position with a single letter, like "R" for "Ranged Goblin" or "M" for "Melee Goblin". Next to each letter I write the number of health the creature has left and whenever it is hit I update the number.
The rough map sketch for myself is important because sometimes other creatures are in adjacent rooms that the players don't yet know of, or there are hidden enemies nearby that will join the fight in a few rounds. In those cases I roll their Initiative, too, and will just interrupt the current turn order once the unseen enemies are joining the frey. Then I will add them to big list that is visible for everyone on the table. When a unit is downed I will just cross them out on my own sketch and the Whiteboard.
You can also use little index cards if you don't have so many creatures or if you have the encounter prepared beforehand. This is especially handy when you have a creature with more abilities, something like a Boss Monster. There you can note the most important things like HP, AC, attack options and treasure - depending on what you perceive as important of course.