I get a "Steam needs to be online to update..." error message every time I start up my computer

Sounds like a Race Condition. In short, Steam is starting up before your network card can obtain an IP address and establish an online connection, so Steam thinks you're not connected to the internet.

You're not the first person to have this problem! I've had a similar issue with my Laptop over Wifi and an old Modem/Router: Steam would give me this error on startup and I could never figure out why - until I got a new router. It turned out that the old router was struggling to output a Wifi signal, and therefore my laptop took longer to connect. The new router, having a more powerful Wifi antenna, didn't have this problem.

Here's what you can try:

Easiest Options:

• Sit closer to your modem. (Obvious)
• Connect to your modem via an Ethernet cord instead of Wifi.
• Stop Steam from starting on startup, and instead start it manually once you have connection.

You can disable steam's auto startup from within Steam. Just got to

Steam Menu->Settings->Interface

and uncheck "Run Steam when my computer starts"

A bit more effort

If you're absolutely hell-bent on having Steam start on startup, you could try:

• Disable startup in steam, and then create a Scheduled Task that starts Steam with a delay
• Update your network card drivers. Sometimes newer drivers have fixes for issues or improve performance.
• Updating your modem's firmware. This is usually pretty advanced (especially for older models) and I don't recommend attempting it if you don't know what you're doing.

You could also buy a new modem, but they aren't cheap and may not solve your problem.