One of my favourite (if not the THE favourite) brand for basics is Petit Bateau, a French brand that actually makes clothes for babies, but they do have a small range of women's clothing too.
The reason I love Petit Bateau is how soft the cotton their basic tanks, tees and undies are made of. And unlike most pieces, these actually get softer and nicer the more you wear them! I love that!
Unfortunately I don't live close to a Petit Bateau shop, so I buy these basics online every once in a while.
If there's anyone out there that hasn't tried Petit Bateau yet, try to at least get to try one of their pieces on, you'll never regret it! Sometimes it actually makes sense to spend a tiny bit more on pieces (even basics!) if you know that you can keep them for that much longer...
(pic from Petit Bateau)