I tried in the game login option but nothing.
How to rent a server?
Try this link, I think it has all the information that you will need. 
Bit confused on what is meant by “slots”. Registration ask how many slots. Not sure what that means.
That is the amount of players allowed on the server at a given time.
Example:
20 slots means 20 players can be logged in at once. You can have as many players use a private server as you want, but only 20 at one given time.
And there is an extra charge per slot? On top of the monthly cost?
Yep, like @ 1 USD give or take a few cents.
That can add up real fast…
IT is not too bad. I think it is like 30 bucks a month for a 40 person server if you do 180 day rental at a time (so 180 USD). You pay for the 40 slots, not the traffic (meaning the number of total players to play or have characters saved on your server).
I would say if you are interested, start with like a 20 person server, see how full that stays. you can bump the number up on the next billing cycle (month) if it starts to gain momentum and gets full.