good advice there from Flowering Rose - there are so many plants to choose from it is worth having a good look around and planning. Right plant, right place is definitely the thing to bear in mind! or you can do as I did when I took on my garden - spend a year or so buying things on a whim and watching in despair when they dwindled and died in the conditions they were growing in! after a while, I learnt to choose what would survive (London clay, shaded for most of the day by houses/ trees in summer, plagued by molluscs, but rarely frosted). There are still lots of lovely things to choose from but borders full of jolly summer annuals aren't really possible! The good thing about a garden is that any wrong decisions can usually be remedied (eventually!) but it can be expensive learning from your mistakes so do take some time to plan. Best time to get planting is coming up in Autumn, but you have time to look around and maybe choose a few key things to get in before winter .
It's also good advice to make the border as wide as possible so that you are not planting too close to the hedge - the hedge itself will suck up an awful lot of moisture from the soil so try not to plant right up next to it and incorporate several barrelfuls of muck before planting anything! Good luck.