I see a number of comments to use a virtual server host, but I have not seen any mention of the main reason WHY this is advisable… If you want to host something from your home, people need a way to reach you. There are two options for this – use a DDNS service (generally frowned upon for permanent installations), or get a static IP address from your provider.
DDNS means you have to monitor whenever your local IP address changes, send out updated records, and wait for those changes to propagate across the internet. This generally will mean several minutes or more of down time where nobody can reach your server, and can happen at completely random times.
A static IP is reliable, but they cost money, and some providers won’t even give you the option unless you get a business-class connection, which costs even more money. However this cost is usually already rolled into the price of a virtual machine.
Keep in mind also that when hosting at home, simply using a laptop to stay online 24/7 is not enough, you also need a battery backup for your network equipment. You will want to learn about setting up a firewall and some kind of IDS to protect the front end of your services, but for starting out you can host this on the same machine as your other services. And if you really want to be safe, set up a second internal machine that you can perform regular backups to, so when your machine gets hacked you have a way to restore the information.
My first server was online for two whole weeks before someone blew it up. Learn security first, everything after that will be easy.