Congratulations on the sale. You don't mention how high you want the fence to be but in windy conditions the most important thing is to install a fence that the wind can pass through to prevent it being damaged by gails and gusts! A picket fence from someone like Jacksons goes up to 1.2m (4ft) and their 'hit and miss' or woven fencing then goes to 6ft. Planting a hedge in front of it is a great idea as this then puts even more visual screening in place. I work in the counties just west of London and see more and more people putting in mixed hedges and having them 'laid' or woven into a pattern- it's a traditional method of installing hedges that looks very natural yet orderly AND because you aren't planting a mono-culture of one species, it's great for wild life. Doing it in Winter is the best time as you will get 'bare-root' hedging at a great price. Do let us know what you end up doing!

I think Photinia would get too large and unruly for planters on top of the walls. They need managing otherwise they get very large and have a very loose form. Personally I'd opt for something that is more consistent in form and shape without too much upkeep and provides an attractive green backdrop to your beautiful house rather than competing with it for attention! Something like Buxus or Japanese box (Euonymus Green Rocket) as alternative to avoid issues with Box blight. Alternatively Privet is a good reliable evergreen hedger particular well suited to urban situations as they tolerate pollution. Either way its worth adding some water retaining granules and slow release fertiliser to the soils to give them a boost. At least you're planting at a good time to avoid stressing them in the dry summer months. Good luck!

I think Sonia is right with the shrubs idea as they would be low maintenance except for an annual trim. Have a search for wall shrubs, these can be easily trained against a wall or fence. This blog has some nice suggestions: https://www.janetbligh.co.uk/5-essential-evergreen-shrubs-to-clothe-a-wall-or-fence/ In addition I’m going to add Cotoneaster horizontalis as it copes with tough conditions but won’t take up much root space. The RHS list it as a non native invasive species however so i would take care to keep it in check. The birds adore the berries tho. You could also grow climbers such as clematis (many varieties) or Jasmine for eg. They need a little help to start with, a support either with wires/trellis or through the shrubs but once they get going they just need an annual trim.

It’s a leylandi hedge that is at the end of its life. The plants only grow at the tips and the inside is old dead wood. It is becoming wider as it appears to already have had a crown reduction so the side tips are currently the active area of growth. You have tried to reduce the width by cutting the sides hard back but the dead Underwood is now visible. This area will not regrow. The hedge does give you a good screening from the other properties around and it will be a big change removing it. However the hedge is not going to improve by further pruning so removing it will inevitably have to be done. You need to decide how much screening you wish to have when it’s gone. A fence would provide some and with layered planting in your front garden you could create a far more attractive screen. Go for it!