Rich, sorry to hear that. I and friends pretty much arranged my partner's funeral last year, completely without religion of any sort. We had the undertaker for the pratical stuff - coffin, cars, slot at the crem etc, and otherwise we coordinated 6 or 7 of us to read eulogies or poems and had music on CD to play (his choices) and I organised the order of service. It was, if there can be such a thing, the best funeral he could have had, everyone said so, and the undertakers took care of all the complicated stuff (including organising a wicker coffin) and were excellent, and we got on with the personal stuff. Go with whatever feels right for you and your Dad. Funerals are as much for those left behind to come to terms with things, and say goodbye, as they are for the dead - so probably good to think about what he'd have wanted, and what you all want.
If you would like any more specific advice, such as I can give, please do PM me, I'll be back online on Monday.