There are some sound source selection issues with system 8.1, but otherwise it is a solid upgrade. I recommend all Twentieth Anniversary Macintosh owners who do not wish to upgrade to 8.5 to use 8.1 because of its stability and features. HFS+, which frees up hundreds of megabytes of hard disk space is worth the price of admission alone. If you choose to only move to OS8, the following instructions still apply.
Copy the items Video Startup 1.6.5, Apple Video Player 1.6.5 and Apple CD-ROM 5.3.3 from your system 7.6.1 system folder to a safe place. Do an easy install (I recommend a "clean" install) of system 8.1 from the 8.1 CD. After you have done this, copy the three items you saved over the new installed versions from 8.1. This will make your machine function properly. Do not do a custom install or you will not get the FM Radio Software. Next install the following updates (available on Apple's ftp servers):
Internet Address Detectors 1.0.2
Quicktime 4.0.3 (Keep MoviePlayer 2.5.1 around for maximum features though unless you plan to pay for Quicktime Pro...)
Macintosh Runtime for Java 2.1.4
Apple Telecom 3.1.3 (Available on the 8.1 CD - be sure you remove objectsupportlib AFTER this install)
Also, be sure to install ATM 4.0.2. This is available on the 8.1 CD.
You will need DiskCopy to install many of these. If you already have DiskCopy, be sure you have version 6.3.3.
Note: If you try to do freeze frame captures with the Apple Video Player 1.6.5 and Quicktime 3.0.x your machine will crash. This bug was fixed in AVP 1.7.2, which removes the tone and balance controls for some odd reason which is why I recommend sticking with 1.6.5. AVP 1.6.5 works very well with Quicktime 4.0.x, which also fixes the bug.
Most of the software updates above will work with 7.6.1, with the possible exception of Personal Web Sharing, Internet Address Detectors, and Open Transport 1.3.1. For 7.6.1 you need to install the following as well as the items above:
Open Transport 1.1.2
Open Transport PPP