The planner won't be able to tell you how big you can go - they won't be able to design the extension for you (ie "go out a bit here, up a bit there"). But they will look at planning history, the size of the original building and any existing extensions and how that sits in the plot of land.
They absolutely can make determination based on style. Sometimes, something ultra modern can be approved - it can show the change between old and new and the passage of time as a building is used through its life - sometimes something ultra modern is out of keeping g with the size, scale and design of the original building.
If the house is in the greenbelt, then there may well be restrictions on size and design.
Best thing is to have a look and see if there are any designations on the house (listed building, conservation area, green belt, that sort of thing). Most local authorities have their development plan online with interactive maps that highlight these. While you are there, have a look for any relevant policies or documents about householder extensions, extending old buildings, green belts etc. It helps to be informed and you can see where the planner is coming from as they talk to you.
Please don't rely on "precedent". Just because someone got an extension of whatever size nearby does not mean it is more likely that you will get one too. Circumstances may be different (change in policy, specific site reasons, design, maybe permission on appeal or by a committee).
The planner will not automatically say no, most are positive about development! It does make a difference if the development takes account of the site, the house and the specific size and/or design.