You should be able to get a full central heating system for that price with radiators in every room. As PD says, shop around
Our first house had hot air central heating and it was marvellous, there was a vent in every room and one over the bath, lovely in the bath and I stood a rack in the bath to dry the clothes -a full load of washing dry in two hours. and no radiators cluttering the walls.
It fell out of favour and got a bad name because builders tried to economise by using systems with just two vents, one in the hall and one of the landing and undersized boilers and it was inadequate and houses were too cold.
But I would love to live in a house with a full warm air heating system again.