What are you asking ?
Are you asking if they're a good idea, asking what types are available, how to look after them ???

Visit and chat with your local nursery or garden centre and see what's available, write down your favourites and then google them for lots of info.

Fast growing evergreens, by their nature, will mean loads of yearly growth and subsequently a lot of heavy and regular pruning if you're putting them in a small garden because they'll outgrow their space very quickly.

a garden center will proberly tell you lalandii, do your self a faver forget it, you will grow nothing else that is any good, Louise is right, but there are exceptions, go on google and type in 1 spartan juniper, 2 sky pencil tree, and then skyrocket juniper, little or no mainteance,for any of them.

I agree - fast-growing evergreens don't just stop when they reach the height that you'd like ideally. They grow outwards and upwards, and will make a small garden feel closed in. Cliffo has suggested some slim trees - I'm going to be different and suggest a trellis against and above your fence - then plant evergreen climbers. You can get some lovely ones that will bring you great pleasure, even in the winter!

For a start, look at Clematis cirrhosa - there are several, and mine are in flower now.

Another good conifer for this is Thuja occidentalis 'Smaragd', A little wider and slower? than the junipers.

I like your surjestion Vincent' but I like Spritzhenry's, better than both our's because the question was about two things we forgot,small garden and privacy,

Good choice Vincent, makes an excellent hedge and easy to control.