Tell us more about the soil as that makes a difefrence. for example, beech doesn't like to have its feet wet but hornbeam doesn't mind heavy, claggy ground. Both will grwo quite fast and dense if kept clipped and can be kept quite narrow too thus saving space. Both are deciduous but keep their autumnal brown leaves if pruned before the end of July.
Hawthorns are also fast growing but are thorny - good for deterring unwanted visitors and protecting birds. It plays host to lots of insects and has spring flowers for nectar and then fruits for birds in autumn.
In the evergreen ranges, yew is good and can be clipped very neatly but it's very dark green and the clippings and fruits are poisonous so not a good idea if you have small children around. Other conifers will grow rapidly but can easily run away with you and do not recover if you clip back into brown wood. Laurel is a thug. The more you prune the more it grows and its large leaves look dreadful when cut with hedge trimmers. Privet is an option if your situation is not too exposed.
As ever, good soil preparation is the key to success so dig a decent trench and backfill with plenty of added compost and/or well rotted manure. Don't buy the biggest plants as they take longer to establish. my hawthorn hedge started as single stemmed whips which I pruned back to 9" after planting. It grows 6' a year which is something else to consider - maintenance.