For the cable connection, the following article could perhaps be of interest.
However, the modem speed is extremely low. It would of course be much better to use a faster modem (something like 14400 bps). Almost any PC-style (DB-25F port) modem can be used with a Macintosh Plus through a Mac modem cable (DB-25M to MiniDIN-8M).
I did not know that it was possible to use a Netscape web browser on a Macintosh Plus (with an external hard drive) computer. There are a few alternatives that work, such as MacWeb (under System 7). An old version of Eudora can (if SMTP authentication is not required) be used for email. You would also need MacTCP and an appropriate PPP program. For details, see the web pages below.
We also had a 300baud modem that we used with our llc. We quickly moved to a 2400 baud modem when paying $6 a minute for a legal bulletin board out of Chicago.
The 300 will work but your top speed for the serial port is 157,000. We had a cable from LapLinkMac that let us do file transfers from our Mac Plus to any PC with a properly configured comm port.
If this is an exercise in 'can it be done' then have fun. If you want to bump up your speed, look at any computer recycler for a faster modem.