ginger - the zeal is what is important, everything else will come surprisingly quickly!! Honestly, a lot of it is confidence - I had a real light bulb moment when I realised that even much greater and more experienced gardeners than I will ever be have failures!!
First of all, that's a lovely big space to play with out your front. You will be able to do something brilliant! Second of all, I'm always on thin ice telling people that "Gardening needn't be expensive" because I can never resist buying a nice plant I don't have. It is an addiction! But for those with greater self-control and willpower than I have, it honestly need not be that £££. There are a lot of places that sell very, very cheap plants - decent stuff, too, not just naff carpet bedding - if you're in the UK, then Aldi, Lidl, Morrisons are all well worth keeping an eye on. And growing from seed is easier than you might think for most plants, and saves a fortune in those cases where you need a big ole clump of something and not just a little bit.
I love your idea of starting with the peripheries, and working in! For your sturdy fence, I guess 20ft is quite a bit of space, and that you can potentially get a few climbers along it should you want to. To fill it quickly, you could either repeat plant with the same climber, which will give you a cleaner, more modern look or mix it up more traditionally, with some evergreen for year-round interest (clematis armandii, tracylospermum jasminoides, the rather amazing winter-flowering Garrya Elliptica 'James Roof' - the latter two need a slightly more sheltered spot if you have one!). I always mean to do contemporary, and faithfully promise DH that I will be restrained, but then my love of different plants takes over and I end up choosing climbers with different flowering seasons because I can't resist the variety! (While I haven't seen those aforementioned climbers cheap, Aldi regularly have climbers on offer for around £1.80, and there are usually jasmines, solanum, passiflora, and various kinds of deciduous clematis).
Hedging on the other side - there are sort of two options that I can see and it depends a bit on how much space you have and how it's configured and how much screening you need from whatever is the other side. Firstly, you could plant something amazing along the boundary (my current favourite suggestion is hornbeam) and then put shrubs in front to soften. Secondly, you could simply use the shrubs themselves as the boundary. The advantage of the former is that it keeps the boundary very clear, gives you a stable and uniform visual backdrop, and offers more privacy with a complete screen - you can control the height. The advantage of the latter is that there is no hedge cutting!! (Again, Aldi just had a range of shrubs in - again, for around £1.80 each - including some rather attractive hollies! I think many stores may have some left over).
A mix of evergreens and deciduous shrubs will give you year-round cover, and if you plan it right, you should be able to ensure you have something colourful pretty much all year. Talking of colour - think about your scheme, too, because you can get suitable things in such a huge range of leaf colours from silver to zingy green to copper! Do you have space for a mix of heights? If so you could even punctuate it with a small tree.
Gosh, I think I'd better stop before I start recommending long, long lists of plants and waxing lyrical about manure and compost mixes. It is such an exciting project, though!