Log into droplet with ssh from 2nd, 3rd, etc. computer

While I have basic linux and intermediate python experience, this is my first time setting up a server and the like. Despite running into roadblocks everyday, I am ecstatic about getting my droplet-website-project-system fully online!

My situation has me bouncing between a couple linux computers and a couple windows computers. So far, I used PuttyGen to make a key pair and can use it with Putty to log into my droplet from one of my windows computers. I disabled password access since that was the recommendation of the guides I used. I would like to be able to also log into my droplet from the other computers, preferably using SSH.

How would I go about doing this logging in from multiple computers? At least, as far as the windows computers go, do I put a portable copy of Putty as well as my key pair onto a USB drive and just run Putty from said USB? Is that secure? Do I keep and use a separate Putty and key pair on every computer?

P.S. I tried to login using the online console. However it just showed a black screen. The webpage said that if I see just a blank black screen then I should click on it and press any key. However, that did nothing as far as I can tell.