Yes, you can install bot on VPS (Virtual Private Server).
VPS is best solution to run the bot because it is designed to run 24/7 and hosting providers usually offer 99.9% up time guarantee, which means that it is very unlikely that your server lose internet connection or be unavailable.
You can connect to VPS from any device (laptop, desktop, mobile, tablet etc.) and control the bot.
We recommend that you use SimplyHosting/Tagadab SVS3000 or better server to run the bot as we are using their servers since 2012. They are fast, reliable and their customer support will help you with any problems that you might get with your server.
VPS must satisfy minimum hardware requirements, those are explained in "What is minimum configuration to run the bot" article.