Nilby I buy from several places but there isn't an alternative to trying on as many different makes and styles as you can because what suits me may not suit you. I like C+C California for their long body shape, James Perse for softness, flat seams, non scratchy label and perfection after multiple washes. RE cheapie ones I have had really good experiences w/ New Look T shirts which can wash really well, when they fade they fade beautifully and they have lots of different neck lines. Petit Bateau womens range T's are fabulous-beautifully cut and they just look stylish.
For people who can wear round necks, Haines and Fruit of the Loom do good, thick and stretchy basic T'.s
A gentle V shape suits most people or a loose low wide V. Uniqlo are good for cotton basics and again ,they have different cuts as do Gap. I always look at the seams-are they flat and double stitched? Are they seamed so the T shirt doesn't twist round the body or end up stretched in a triangular shape?
American Outfitters have good T's but I avoid H&M-their T's seem priced very high for their very poor quality. New Look's are more reasonable. M&S do good basic V neck and slash neck T's especially from March when the summer stock drops. I have long sleeved v neck and round necks from there that are eight years old and because they have a little lycra in them, they have not lost their shape. The basic long sleeved T from Laura Ashley are good quality too.
Of course I have to replace white T's several times a year as they never stay white. I like them either tissue paper opaque or in a Winter weight cotton like the Fruits of the Loom ones. Also keep an eye out for decent Thermal T's-the Men's undershirt white thermal T's in a tiny size wear well as do the M&S thermal T's. They have a rib weave that doesn't stretch out of shape.