The typical cost of the horse for general family use is the cheap part, £1000-4000 the up keep ongoing monthly costs livery etc.. 200/300 a month depending on if you have full livery or DIY etc....... big commitment. easier of course if you have room on your own land for a stable/ paddock.
A good way to start is to go to some local livery stables local in you area, most have riding schools attched, most will know a horse dealer or can advise further or maybe assist in locating the type of horse, size, ability (jumping, showing, or just a family hack ?) .
If you sell on the horse a year or two down the line,if the family outgrow a pony etc then its typical you should get your money back, but the cost as I said is the small part as its an ongoing expense once you have it.
make sure the family if they are not experienced riders get a horse that is bomb proof. Cost will vary depending on how far the horse is broken in etc how old 5/8 year old should be o.k. ? Make sure the horse is also very o.k. at having his feet lifted/ picked out. and not skatty on that front. Its not fun worrying about half a ton of thrust coming your way when your thinking look here horsey im only cleaning your hoofs.
Get public liability insurance for hacking in public, insure the horse and look into vet insurance.
Also when you locate the horse, espeically if through a dealer or school ask for a few weeks trial,whereby you and the family will interact ,look after and ride it (maybe at the local horse school) , they should be helpful towards you.
Good luck , enjoy.
Oh if you yourself have a lesson at the school make sure the farmers not outside and firing up his chainsaw. Horse's sometimes dont react too well to chainsaws.
