I spent several hours rolling through more than 10,000 employees to try and find the upper limits of what their stats can be. Figured I would post the results.

Ticket Masters control your ticket computer allowing you to do other things. Their maximum stats;

Efficiency: 300%
Precision: 100%
Speed: 7
Endurance: 400
Break: 30

You can find a "Star Employee" named Caylus for $250/day, his stats are;

Efficiency: 400%
Precision: 100%
Speed: 5
Endurance: 300
Break: 36

Would highly suggest finding Caylus, he can run the computer all by himself all day long without anyone ever not getting a ticket. By the time you can get him, his break time is half the timer before someone leaves for waiting to long.

There is a considerably lesser option... another "Star Employee" named Hugo. For $400 you get;

Efficiency : 300%
Precision: 90%
Speed: 6
Endurance: 250
Break: 36

Cleaners are your bread and butter, in general at least half your employees will be cleaners due to the shear amount of "cleaning" that needs handled in the game... not least of all the damn puddles.

Maximum Cleaner Stats;

Efficiency: 300%
Precision: 100%
Speed: 7
Endurance: 400
Break: 30

As before, there is a "Star Employee" cleaner, his name is Travis. His stats for $700 are;

Efficiency: 360%
Precision: 100%
Speed: 7
Endurance: 330
Break: 105

I think Travis is worth it... but maybe not right out of the gate. The $700 pricetag and his 105s break really hurts his value. You can get someone almost as good at less than a quarter the price usually. Save him for last, that way you have 3-4 other Cleaners for when he is on break.

Having a Maintenance man is up to the player, by the end of the game it takes a VERY long time for things to break down and you can essentially only do repairs once a "week" if you want to. That said, their maximum stats are;

Efficiency: 300%
Precision: 100%
Speed: 7
Endurance: 400
Break: 30

There is a "Star Employee" maintainer, his name is Patrik. For $250/day you get;

Efficiency: 300%
Precision: 100%
Speed: 4
Endurance: 360
Break: 35

By the time you can get him, Patrik is a very solid pickup, the only thing that really sucks is his speed which again... won't matter much as things very rarely actually break down by that point.

While you don't NEED a Lifeguard... they sure do make life a bit easier. Saving people is not that bad, but CONSTANTLY having to push people off diving boards gets old very fast as the diving boards get higher and more intricate. The maximum stats for Lifeguards are;

Efficiency: 300%
Precision: 100%
Speed: 9
Endurance: 400
Break: 30

There are two "Star Employee" Lifeguard options, Calum and Sophia.

Calum $500
Efficiency: 220%
Precision: 100%
Speed: 7
Endurance: 300
Break: 45

Sophia $200
Efficiency: 200%
Precision: 100%
Speed: 10
Endurance: 250
Break: 0

Sophia certainly appears to be the better choice. Her break timer might be a bug, and may get patched in a future update, but for now... she is the only character I saw with a speed of 10, and she never goes on break... if you pick her up she is the only Lifeguard you need.

Restocker's are a quality of life hire, you don't need them at all, especially if you have 8 other employees. That said, once you have a 5-star park, and having a half a dozen of each vending machine in the park, they can certainly keep you from having to run around like a chicken with your head cut off. Their maximum stats;

Efficiency: 300%
Precision: 100%
Speed: 9
Endurance: 400
Break: 30

I did not see a star employee for restocker, doesn't mean they don't exist or won't in the future.

The vendor will run your food/drink stand for you. I personally don't recommend them at all as you can just put your vending right in front of the stairs. This allows you to handle vending while watching those coming into the park for cheaters, drunks, etc. Also allows you to see most of the park looking for pervs. Also the vending is just too easy if you have 8 employees handling everything else. Maximum stats are;

Efficiency: 350%
Percision: 100%
Speed: 7
Endurance: 400
Break: 30

There are THREE "Star Employees" for vending... I am guessing one for each stand.

Alex $20
Efficiency: 110%
Precision: 100%
Speed: 2
Endurance: 200
Break: 18

Igor $150
Efficiency: 275%
Precision: 100%
Speed: 5
Endurance: 481
Break: 35

Nick $100
Efficiency: 300%
Precision: 25%
Speed: 7
Endurance: 360
Break: 27

If you get lucky early on then Alex could be a solid option for you and super cheap. Otherwise Igor would be the best option... or you run both of them and you handle the third stand as Nick is worthless.