Greetings and welcome - great to see a young musician interested in jazz
Best place to start, imho, is an excellent, free online course from Berklee College of Music called "
Introduction to Music Production". Covers the basics of DAWs, tracking, effects, etc. Six weeks long, next session starts tomorrow. You will need a DAW for the course - don't use something you find cracked on the net, often unstable and prone to crashing. Get a copy of
Reaper, which is fully functional for a 60 day trial. Actually, it never expires, just keeps bugging you to pay up. Make sure to check out the great
tutorial videos, as well as the active
user forums. Many sax and brass players there you can learn from, friendly place.
While you take the six week course, find a part time job 'cause you're gonna need about $300 to get started
Although your mic will be good enough for the course, you won't be happy with the results musically. You will need a more suitable mic, mic stand, audio interface, and a decent set of headphones (monitors cost more $ and can come later). My equipment suggestions:
Shure SM57 - decent and versatile mic, works well on sax, brass, reeds, can be found on eBay for around $60.
Mic stand - good ones are quite expensive, but you can get by with a cheap one from On Stage Stands. $30, just throw some weight on the tripod base - and an
SM57 is pretty indestructible anyway.
Mic cable - don't waste money on expensive cables, this one from Hosa will do fine
Audio interface - Focusrite Scarlett Solo, at about $100 afaik the lowest price decent quality interface.
Headphones - AKG K240 - about $100, very good quality and accurate.
So, you're looking at a little under $300 to produce high quality work - but you can certainly give it a go with what you have. Also, the equipment recs are just my opinion, probably want to finish the course and do your own research before buying anything. Hope this helps!