Really, try not to worry (I know this is easily said). We are quite tight for money with the school fees. Our children go to schools where some parents are extremely wealthy. They are people as well, they love their children as well and they want their children to make friends and be happy.
The reason I suggested a room in a pub is that it is one step up from the church hall so looks really nice but most importantly, they can serve pizzas /chips for the children (less for you to worry about).
We always had Prosecco for the adults (and a non alcoholic alternative). The parents often want to have a chat to other parents, especially in a new school (I did). Everyone want their children to find friends and I (and many I know) like to know that the other parents are sensible. I liked to watch the children play together before a play date at that age.
The entertainers we have had have been “science party” or “bubbles” followed by party games like “musical chairs”, pass the parcel”, etc. We do more activity parties now, climbing parties have been a lot of fun.
Party bags we try to do very cheap. If is is a bubble party, bubbles, some stationary with bubble theme and some sweets. At that age children seem to be excited over many small things.
Please try not to worry too much. One of the friends of my youngest DD has very wealthy parents (live-in staff and swimming pool). We live in a small flat and I do all the cleaning. I don’t socialise with the parents but we are all really happy that our DDs are friends. They are two little girls who get along really well, like to draw, be silly and can spend an afternoon without an iPad. We also know that neither child has unrestricted access to the Internet (inappropriate materials is a big worry).
I have some good friends among the parents as well but sometimes people are just too different. That doesn’t mean the our children cannot be friends and that you can’t have an interesting chat over a nice drink at a children’s party.