This sounds like you should be approaching Kevin McCloud (Grand Designs) as a lot of the people on there have normal day-to-day lives and have no or very little knowledge of the construction industry and process. No offence to you by the way.
does it cost anything to send plans for a house to the planning office or is it just architect fees if you go that way?
Nothing's for free in this world. It all costs and with regards to planning AND Building Regulations, the fee's are normally based upon the number of units (i.e. houses) you provide.
As well as local authority and professional fee's (i.e. architects), for a new house, you'd be looking at many more reports required, which would be required to submit as part of the planning application (e.g. Design and Access Statement, Renewable report, etc...). They may also request contributions in the forms of payment towards local government sectors (e.g. SPA's, local amenities, etc...).
And with it being a new house, one would assume you'd like to take our warranty protection/insurance, which again would be more fee's and the NHBC is one who'd provide this. They base their fee's on the works involved, your previous and financial background, etc...
There's A LOT to it.
My advice is to engage an architect and they should be able to tell you all the above plus more