Online golf scorecard

HI,
We want a online golf scorecard for a crazy golf course.
Happy to lead with your advice on coding language however if it could be within wordpress it would be preferred.

Basically the course currently gives out each player a physical scorecard. We want to get rid of the print and make them all online.

The player would go to the website.
They would then either login or start a new game.
They would need to select how many players and give each player a name.
Click continue to be shown the hole one information and a list of each players.
Next to each player would be a text field to add each players score. If possible next to which would be a total field which would add up each hole whilst they are playing (so they can see who is in the lead).
Once a hole has been played they would click next to go to the next hole etc
On completion it would although them to save scores to their account, create a account if they dont already have one etc.. also show who the winner was.

We would like a highscore link on the site so that we can run monthly competitions for the best players.

I hope this makes sense?
I can give more information if needed and also sketch some ideas down.

If this could be done within wordpress we get the staging link setup and also help with design.

Would this need to be a full build or custom module within wordpress?

Dont know budget yet.

Thanks