The world is your oyster. The way to go in my book is dependent on your location, soil type, evergreen or deciduous, seasonal or all-year-round interest. I would look around at what neighbours are growing to see what you like and what thrives in your area.

Are you able to add a photograph of the area/garden? What you plant also depends on how much space there is available...

See if your local library has or could get for you the Royal Horticultural Society's Enclyclopedia of plants and flowers.
It has a large section on shrubs which subdivided by size, flowering season and blossom colour so you have an enormous choice, with the opportunity to check the eventual size of each plant. If none of your neighbours has an azalea or a rhododendron and you want some, the reason might be the soil, so invest in a cheap pH metre from your garden centre to check that your garden is acid enough for them.

I would remove the turf before planting permanent plants like shrubs. The grass will just be a pain. If you want a curved border lay out the garden hose until you get a shape that pleases you. I would plant a framework of evergreen shrubs then interplant with deciduous ones. If you can get a hold of it "the Dr Hessayon book of Trees and Shrubs" is very easy to follow and will provide you with all you need to get started. It sounds like an exciting project. All of the advice given by other members above is good. do let us know how it goes.

On a large expanse of lawn I would put in a largish kidney shaped border and include a couple of medium sized circular beds, in these you could plant some decent small trees that give plenty of interest through the seasons, here a few ideas, betula utillis, the Rowen,Chinese rain tree, and the forrest pansy think it’s called cyphydillian, not sure on the spelling, in the large bed plant out with plants that give interest throughout the year, a selection of Hebe, include some evergreen shrubs amongst some deciduous ones, it all depends on the size of the bed, a large bed then some of the following would suffice, ceanothus, spireas, exocorda (the bride) witch hazel, Berberis Darwini and thunbergii continues, euonymus alatus, calicarpa, small plants for edging ophiophogun heucherus, a small to medium bed on the the lawn that would contain a group of cornus with midwinter fire being given pride of place, would fill you with joy in the depths of winter underplant with various spring bulbs.

To add to the sound advice given above check under "S" in the Goypedia pages below. There are lovely photos of plants grown by our members. I would recommend you remove the turf before planting anything. Grass growing through your plant roots will not be good for them. To decide on the size of border to have, lay your garden hose along with maybe an odd curve until you find the shape that works for you. Plant a background of evergreens then grow deciduous plants in between. A book named "The Tree and Shrub Book" by Dr Hessayon should be easily available. It will explain all you need to know about how far apart to plant etc. If you need more advice come back again and do keep us up to date on how your project is progressing. excuse the reply given twice. It took so long to upload the first one that I had another go.