Well that is an interesting picture.

I can assure you that hanging wall gardens are all the rage and that is a great idea but they can also be high maintenance if exposed to high winds / sunshine etc. I have seen some lovely fake ones that would do just as well. You could also have a few pots with additional greenery. As you say your view is not "great" maybe you can have a creeper in one of the pots that can weave its way through the railing. I probably wouldn't go for one big chair as it could dominate the entire space. I would consider a table with a couple of fold-able chairs .... something that is comfortable, inviting if you have friends over but can be placed in a corner if you just want to open up the space. I do not think you need a carpet and but maybe some fancy outdoor tiles will look just as nice. You want it to be easy care and weather proof.

Do you need or wish to incorporate a washing line? A pull out one from a wall will be perfect that way you can retract it back when you are not using it.

If you deck gets too much sun, you may want to consider some shade shutters. I have seen them called 'plantation' shutters.

GOOD LUCK

What a lot of good suggestions from Bernadette! Go for small single items of furniture that make minimal visual impact - eg, fine 'wire' or steel rod furniture. Greenery is a must I think. You could hang window boxes on the outside of your balcony rails so as not to encroach on your space. If the view is not great add some taller plants or even wires or screens for clambering plants. Think about lighting.

Place couple of chairs and small table at one end and 3 pots at the other, along with planters along the front of the railing, pierced metal candle sconces on the walls and you're made!