I have a machine that I use only to browse the Internet. What if I blocked all ports on this machine (inbound and outbound) except for port 80 and port 443, and restricted these two ports to an internet browser executable. Would this make my machine more secure?
First, it might make your system slightly more secure but it does not make it fully secure. In the majority of attacks today the victim unknowingly invites the attacker implicitly into the local network. This is for example done when surfing the web: all content you visit is downloaded to your local system and rendered or executed (depending on the content) there. The same is true for emails - any attachments you open will be opened on your local system. And attached Office documents, PDF, archives etc are typical vectors to infect your system. No firewall which just blocks based on ports will protect you against these most common attacks.
Apart from that you should only block incoming ports for data which are not part of an established connection (initiated from the inside). Otherwise you will simply not be able to surf the web anymore. And websites are not only located on port 80 and 443, so restricting outgoing access to these ports will probably result in over-blocking too. Similar you might need access to other ports like 143, 993, 465 ... to retrieve and send mail (unless you use web based mail). And games or whatever applications you use might also need different outgoing ports.
Depending on what system you use it might the best (most security with less side effects) if you use the systems capabilities. For example if you declare your computer to be inside a public network it will already adjust the firewall accordingly to not allow any incoming connections but allow outgoing connections.