Most of the time when I open Safari it doesn't connect to my opening page. The bar goes just so far then stops. I have to restart my computer in order for it to open. I have a MacBook Pro with Catalina v10.15.7. Any suggestions?

Go step by step and test.

1. Update Safari, if an update is available. Update may come with bug fixes.

    https://support.apple.com/en-us/HT204416

    https://support.apple.com/en-us/HT201541

2. Quit Safari, launch Safari holding the Shift key down.

    https://support.apple.com/en-us/HT203987

3. Startup in Safe Mode. https://support.apple.com/guide/mac-help/start-up-your-mac-in-safe-mode-mh21245/mac.  

    Quote:

    It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. 

    And it deletes some system caches, including font caches and 

    the kernel cache, which are automatically created again as needed.

4. Clear History

    https://support.apple.com/guide/safari/clear-your-browsing-history-sfri47acf5d6/mac

    Please read the article before clearing history, 

    this is like a low level resetting of Safari without affecting passwords and bookmarks.

5. If Safari doesn't open a webpage or isn’t working as expected

    https://support.apple.com/en-us/HT204098