Yeah, you don’t need to manually stop and start your dynos. Heroku will shut them down after a period and bring them back up when someone tries to access them. To the user, there would be a significant delay. You can prevent this by upgrading your dyno for $7/month. The problem is that you’d have to pay that fee for each dyno you want to run, and this doesn’t scale very well for you. DigitalOcean is a far more cost effective solution because you’ll get charged for what you use (I always get charged the $5 minimum and not much more), and you can run as many apps on your rented machine as you want. The trade off is that you have to learn some system administration to get your apps uploaded, routed, and running.
Frankly, I think the best option for now is to stick with the free dynos. Glitch is another option. If you want to learn how to get your apps running on a real server, start with VirtualBox and Ubuntu for practice and learning. Beware, though, that this is a very large topic and you’ll have a lot to learn. Here’s an older video that shows the install process: