I am thinking of getting a modem and router and a WiFi device,but i don’t know which one.
Which one is the cheapest?
My first step was to have internet access installed
An Internet Service Provider (ISP) installed a modem/router box
connected to my cable tv outlet.
No charge; it’s included under my monthly internet payment
The router also provides local Wi-Fi
For Wi-Fi devices, I have a Mac Mini desktop computer, and a iPad tablet
It depends on your internet provider and what is compatible with them. Also, what kind of internet speed you’re looking for.
I currently have Comcast Xfinity and they charge $300 a year ($25 a month) to rent theirs. I also have the bare minimum WiFi (200 gbs) because I live by myself and don’t need more than that. So, with that information, I decided to buy my own modem and WiFi router for less than $200 that I can sell if I ever move. The upfront was a lot, but, within a year, I’m saving $100; in two I’ll be saving an additional $300. If I sell it, that’s another $100 back in my pocket. I can share what I got if you have Comcast Xfinity.
what i have optimum 
I wouldn’t know for Optimum. You’d have to get in contact with them and ask them for a list of compatible modems. They may have it on their website.