Here is my not quite current list of updates/patches for Windows 98 Second Edition:
Internet Explorer 6.0 Service Pack 1
Microsoft DirectX 9.0
Windows Media Player 9.0
MSN Messenger
Apply the following patches in the order listed. Each patch needs to restart the computer.
Q238453 Windows Security Update 1, November 29, 1999
Q245729 Windows Security Update, November 12, 1999
Q256015 Windows Security Update, March 17, 2000
Q259728 Windows Security Update, May 19, 2000
Q260067 Mapped Drives Shutdown Update
Q273017 Windows IDE Hard Drive Cache Package
Q273991Windows Share Level Password Update
Q318203 Windows Security Update, February 13, 2002
Q313829 Windows Security Update, March 07, 2002
Q314147 Windows Security Update (Unchecked Buffer in SNMP Service)
Q323172 Windows Security Update (Certificate Enrolment Flaw)
Q323255 Windows Security Update (Unchecked Buffer Vulnerability)
Q329115 Windows Security Update (Certificate Validation Flaw)
Q329414 Windows Security Update (MDAC Security Hotfix, 06-Nov-2002)
Q330994 Outlook Express Cumulative Patch, April 2003
Q813489 Internet Explorer 6.0 SP1 Cumulative Patch, April 2003
Apply the following patch if you experience shutdown problems:
Windows 98 SE Shutdown Supplement