Should we begin life in Poland by just using our English bank card for transactions in shops etc
Yes, but be careful about charges for overseas use. Have a look on moneysavingexpert; they compare cards for using abroad. Basically MasterCard is always better than Visa and the best card to use by far is the Halifax MasterCard.
Or should we leave all of our savings in a UK bank account and transfer an "amount" every month to our Polish Bank to cover us for the upcoming month then use our Polish bank account.
This is usually better. If you have a Polish account that receives GBP (most do) already, Transfer it, withdraw the cash as you need it and change at a Kantor if the rate is much better than the bank. If you don't have a Polish bank account yet, use a MasterCard or even better, bring plenty of cash and change it here.
It's generally a good idea to keep your UK bank account, especially if you have any income or payments to make over there.