plan to drive ourselves around Poland in a big circular route
Be safe, Poland has a terrible road safety record you'll find that there is a low compliance with basic road safety regulations, poor infrastructure, mixed traffic i.e. lots of freight trucks, competing with farm vehicles and luxury models on single lane carriageways, linear villages, drink drivers, and under-performing emergency medical and rescue services and a general lack of awareness and disregard about the importance of road safety.
Do you recommend gas or diesel automobiles?
Diesel for sure. 2.0Litre diesel engine should cost you around 6 Litres per 100km.
Is diesel fuel readily available throughout Poland?
No problem. There are filling stations are in every town, and some villages too.
Will we need to have lodging prearranged throughout the trip or should we be able to find lodging as we proceed from stop to stop.
If you are coming over in September most, if not all, hotels will have vacancies.
If we avoided Warsaw completely, would we regret it later?
I think you would, it might not be Polands most attrative city, but check out the old town (stare miasto), there are plenty of museums, parks, shopping malls to see, etc.