Updates fix security problems, so they matter. Take a backup before you update, update a few plugins at a time, and check the site after each batch.
Every plugin you delete is one fewer thing to keep up to date. Deactivated plugins still sit on the server, so delete the ones you no longer need.
When something goes wrong, a calm, practised restore gets the site back quickly. Work through these steps in order.
Keep a note of when the backup was taken, so you know which changes need to be made again afterwards.
A backup is only useful if it is recent enough to restore from without losing work you care about. The right backup schedule depends on how often the site changes.
A brochure site that changes once a month is well served by a weekly backup. A shop or a busy blog that takes orders or comments every day needs a daily backup at the very least.
A backup you have never restored is a hope, not a plan. Restore a copy to a test site every few months and check that it works.