
Must echo the advice on buying absolutely the BEST instrument you can afford.
Though I don't play sax (I can a bit and I love it, i just don't own one/havent properly learned), I play flute and a variety of other things..
Skimping on an instrument cost is a really false economy - the cheaper end of the range, the lesser known makes, the nasty cheapy stuff - isnt THAT cheap to start with and has no resale value. So IF you give up, and want to sell on, you are pretty much wasting your time, as compared to reselling a well known and trusted make such as Yamaha, which will hold its value much better.
After that concern (which never concerns me because I don't sell musical instruments, it would be like selling one of the dogs!) - you just do not get as good a sound from these cheaper brands as you will out of a good quality one - and that makes a BIG difference at beginner level, which is something so so many people (especially parents of young kids learning an instrument) do not realise. Learning an instrument is HARD, and if the poor quality of the instrumenti s holding you back, if the sound is not wht it should be, that is incredibly demoralising!
Go to lots of shops, play lots of instruments - do not entertain shops that only sell nasty 'no ones ever heard of it' makes and none of the top end makes! Similarly if they wont let you get the instrument warmed up properly and have a good go.. walk away. (And try not to feel self concious in a shop trying something out!)
Annnnnnd unless you are REALLY up on your knowledge of the instrument and have played a lot of them, don't buy second hand or even new.. from ebay. Lots of fakes, lots of nasty stuff about.
I have to say, i have come back to playing the flute after a 15 year break (mostly enforced by the theft of my gorgeous Yamaha flute), started out with a second hand £25 job off Ebay (ha, see, learn from my errors). Its actually not 'bad' but it needs a service which ive not gotten round to having done in nearly three years. I found it very demoralising and hard work to play...... so saved up and bought a handmade wooden flute, ergonomically designed for the smaller handed player, shipped over from america... Ok so it set me back well over a thousand pounds all told and it took 6 months from ordering to it being completed and sent out, but BOY was it worth it. I now play every day and I uttelry love it. IT isnt an easy job relearning on a wooden, keyless flute, but when i get it right the sound is magical, really awesome and actually everything I had hoped it would be (and wasnt) when i first started playing aged 11 (because i was learning on a horrible heap of cast iron junk!)
So, sorry to waffle but investing in the best instrument you can get after a lot of research is absolutely the thing to do!