When you say, "small web app that you are hosting from your home lab", we would also need to know whether this web app will serve real users? Does it have a commercial or semi-commercial purpose or it is purely experimental? Is it ok if your web app remains unavailable for extended periods of time?
If the answer to the above question is, "no, my web app cannot remain unavailable, it has to be accessible 24/7", then you can't host it at home.
Second question to answer: do you have expertise in setting up a web server, system administration tasks and database management systems (backup, recovery, performance, etc.)?
If the answer to the above is no, I would suggest that you take Amazon servers. To be precise AWS cloud servers.
They have something called a "free tier" wherein you can use 3 servers completely free of charge for one year. The limitation is that these servers have to be machines with not more than 1 CPU and not more than 1 GB RAM. These are called "micro instances" in AWS-speak. So, you have your DB server (MySQL, since you wouldn't want to buy a commercial DB license), an application/web server and one more server to spare.
BTW, Interserver offers databases as a "managed service" where they take care of everything - backups etc. You can just start using the DB without worrying about installation and other hassles.
And btw, even after your 1-year free tier expires you can "switch on" those servers only when you need them to be up and "turn them off" when you don't want your web app to be accessible. You only pay for what you use. However, a disclaimer: look up "elastic IPs" and why you might need them (or may not need them).
Considering that you speak of a "home lab", I would recommend AWS micro instances under the free tier. Go for it.