Once you have binned all your instant coffee the next step is to acquire some ground coffee. This takes a bit of experimenting. To be honest most of the quality of a good cup is to do with the making more than the coffee, but there is some variation in the market.
It's fairly standardly sold by strength of coffee on a scale of 1-5, three is fine though the occasional 4-5 is worth it especially after dinner with some dark chocolate.
I drink for the taste more than the caffeine so you can go for decaf if you want. Grounds like Tesco's own brand are perfectly fine. A bag of Starbuck's Verona will serve you well. A good coffee drinker will get through bags of coffee fairly swiftly so you can afford to experiment a bit, go with the deals, go with what sounds interesting until you find some that you like. It feels more expensive, but compare the price at home with the price in a coffee shop and it's bargainous to drink good coffee at home (not to mention business-genius by Mr Starbucks and co to get us paying so much per cup in their shops... ).
update: I overlooked the question of Fair Trade coffee, see comment from Tom.
The other option is to buy beans and get either a hand grinder or an electric one. This certainly adds freshness but does add effort. With a hand grinder you'll be immersed in coffee aromas before you even boil the water. Once bought, store in the fridge, or in a sealed container - I use a couple of air tight tins, one for decaf and one for caffeinated.