i have 3 john lewis own brand stainless steel saucepans and they're worth every penny. they range from about £15 to £25/30 per pan, depending on the size. i bought them separately rather than in a set so that i got the sizes i wanted. i also have a large aldi non-stick frying pan with lid which cost about £12, and that too is great. personally, i would never buy non-stick pans after using stainless steel, but would always buy a non-stick frying pan.
it's probably nothing to do with your saucepans that the meat isn't browning, you're maybe fiddling with it instead of just putting it in the pan, leaving it alone then turning it once and leaving it alone again. all the messing with it does something to it and it will never brown, just go grey and steam. of course it's different with mince or stir-fry where you have to keep stiring it, but i guess you're talking about a steak-sized piece. and maybe you're not cooking your bubble and squeak long enough to crisp it, perhaps too much in the pan?
anyhow, they're my thoughts, hope they're of some use to you :)