I have lots of personal transactions that I don't want appearing as an expense. I have set up "spending" in owners equity, but the transactions still appear in expense?

It's good that you've already created an equity account, MrMiyagi. However, there are two scenarios that I can think of this.

If you borrowed your personal funds to pay your business expenses, you can reimburse your self via cheque or an expense against your business account. If it's the other way around, you can reimburse your company via bank deposit.

The article about mixing personal and business funds can guide your to record your transactions.

If you need more help. feel free to give short reply below.

My QB file is for me personally - to help me keep track of my finances and also assist with recording claimable transactions.

When doing a P&L, the "spending" account doesn't show, which is good. However, when I click "expenses", they do show there which is annoying as they outnumber actual expenses. 

Is there a way to remove them from showing in "expenses"?

I'm glad to know that you're using QuickBooks to track your personal transactions, MrMiyagi.

The P&L in QuickBooks Online will show all your expenses whether they are personal or claimable. However, you can re-assign your non-claimable transactions to a different category, then deselect it from the report.

The screenshot below shows how I deselected the Personal Expenses account I created.

On other hand, to re-assign your transactions, you'll want to change the Expense account assigned to your items. Then, select the option to affect your historical transactions, so you won't need to go through each of them.

If you directly used expense accounts on your transactions, you need to go though each of them. 

You can always go back to this thread if you still need help with your report.