rich p said:
I can't read music - is that a surmountable problem with a bit of effort?
Not at all. If it's an alto sax you'll only need to learn the treble clef anyhow, unlike say playing the Piano where you need to learn both.
You can learn to play by ear, it's a bit a bit like learning to speak a language without being able to read it and I would think it a bit limiting and slower progress.
Last lesson teach brought a book of 'Tunes from shows' for warming-up and sight reading practice and I could play most of them pretty easily, in fact once I'd got a few bars on some of the tracks I could almost play them by ear, but I'd needed the first few lines to get going. Also say the well known riff to 'Pick-up the pieces' is written more complexly than you 'think' it sounds.
I can just about play 'Take Five' and that would take me a long time to figure out by ear even though I have pretty good pitch.
Go the whole hogg, get lessons, learn to read music. It's like learning to ride a bike or learning to read, once learned it stays with you for a life-time.