In your place, I would sort the papers into two groups:
confidential
others
Anything confidential in the legal sense, in that it was part of your work and you signed a confidentiality clause must be destroyed, as you know. If this pile is too large for your shredder to cope with, or if it simply would take too long, contact your employer (former or present) and ask their advice about destroying these documents.
Unfortunately, not all the firms that claim they destroy confidential papers properly actually do so - confidential papers have been known to crop up in land-fill.
You may want to include things like former drafts of your will in the confidential pile.
The rest, including bank statements and tax returns that are older than the Inland Revenue can demand to see, or that you will need if they should demand an audit going back some years, you can safely put in the recycling bin for paper.
However, if as I suspect, you may be intending to move to a smaller property, do make sure you do not destroy now any receipts for work done on the property, or for items you may decide to sell, rather than hang on to.
If you have more than can go in the recycling bin in one or two goes, which is likely, ring the recycling plant and find out whether you can hand the rest in in plastic sacks, in paper sacks or baled, and if they will collect it, or if you have to take it to the plant
And do remember to remove staples and paper clips from anything you intend to shred, as no shredder can cope with metal.