Self hosting is perfectly viable, if you know what you’re doing and consider the specifics. Apart from the computer specs and the installation itself, it’s important to consider that:

• Your server should be connected to high-speed, low-latency internet 24/7.
• As the site grows, connection throughout is even more important - think about, say, a popular member of your site publishing a video and 100 followers coming to watch at the same time due to notification. 
• Your connection should have high UPLOAD speed to cater for the above. At least 100Mbps is recommended. In Australia connection like this is going to cost at least $100/month if you’re lucky to get one - negating any savings from self-hosting. It may be different in your country/town. 
• Make sure to setup off-site backups. Your computer may easily fail if it’s not a server-grade hardware servicing multiple connections 24/7. Also insurance may be in order.
• In most cases SSD is best for web server - more costly, but makes big difference in performance.
• If your target audience is not within same locale as your hosting provider then network bottlenecks may be an issue. 

IMO by the time you factor in the above, remote hosting may work out to be more cost effective. If, however, your site is at early stages, your work computer is running anyhow, you have cheap good internet connection and your traffic is mostly local - self hosting may be a better option at first. perhaps you can even find ways to scale it up efficiently.