Abraham said:
i played alto for a good few years, still have it and can play but very very rarely do
i think it's the most accessible and has the widest variety of music written for it
Ditto (scarily, to everything

).
I played alto for about 9 years, started studying for grade 8 but decided to not go for it as A-Levels were looming. I then went to Uni (and graduated last year), and havent really played properly since.
Alto is what you'd get started on if you were young-ish, however if you're ~16+ you might ask about learning tenor. Since probably doing my grade 6 i wanted to move onto tenor as it just has a nicer, fuller sound. But because i started very young i physically couldnt play the tenor (hands not big enough etc.) The tenor i'd say is more widely used by solo artists and saxophonists in jazz combos/small groups (of course, big bands mostly have alto as well as tenors).
I just spotted your question: Is it a good idea to get lessons! Of course! You honestly wont get too far without lessons, unfortunately. It's possible but it will make it such a steep learning curve to learn how to read music, learn fingering, and all the other skills you need to play the sax. Look out for sax teachers that teach jazz. I was never interested in playing anything other than jazz, so that's what i did. (Incidentally, part of the reason why i stopped lessons was because my teacher went off to tour in his band

).
Maybe go into your local music store and ask about sax teachers. Pick one you like the sound of an arrange a meeting. They'll let you have a bit of a go (probably on different ones), and you can have a chat about what you want to do.