I hope you and your family will be very happy in our country. It is a wonderful place to live.

Generally speaking you will probably find it very difficult to buy a plot of land with enough for a smallholding with the intention of building a house on it. You'd be better to buy a house with land attached (and suffer competition from horsey people) - or a house and separate land although that is not ideal with some animals that may need you to be close by overnight.
There is a difference in the house buying system too - we have 'offers over' rather than a suggested price, and the amount you pay can be a) roundabout the offers over price, or slightly less depending on how long it has been on the market, or b) a percentrage over the offers only price, depending on what area you are buying in. That can vary from say 5% to 20%
There are a variety of methods of looking for property, but for houses with land the likes of Shepherds, UKlandandfarms, (
http://www.uklandandfarms.co.uk/rural-properties-for-sale/scotland/central-scotland/) or the agricultural auction sites (Aberdeen & Northern Marts for instance) are possibly better than the standard estate agents. Some lawyers have their own estate sections too, so probably googling "houses with land in Dumfriesshire" or something similar might get you rolling.
As to PD, I'm not au fait with acronyms, but if it is subsidies you're after, I would suggest the house and land are the first thing you should consider, as that will be the most difficult to find unless you have a considerable deposit and/or mortgage available.
Good luck!