Mountaineering is not a joke and should not be taken lightly. Being well prepared will make your experience far better, and reduce the likelihood of others needing to risk their lives to come rescue you.
You need at a minimum-
A brain.
A good partner who also has a brain.
Rope
Crampons
Good insulating boots. If you like your toes, get good boots. Your boots may be fine for walking in snow, how about a bivouac? How about being stationary in a storm on the side of the mountain for 4+ hours? What are your toes worth to you
Helmet
Harness
Decent metal shovel for tent platforms and emergency shelter
Axe appropriate length- a 5'10" cat uses about a 70cm axe
2-3 prusiks- I bring two 18 foot Purcell prusiks and two 6 foot loops to make additional prusiks
About 5 biners, at least two locking
1-2 snow pickets
1x pulley. If you can get a self tending one, great. If you aren't sure what that means, you're not ready yet.
Wands to mark your trail.
Learn how to prusik, how to set up a 3-1 or z-drag rescue system, and glacier travel. Mountaineering: freedom of the hills is basically the climbers bible.
If you have any questions PM me. I have done most of the big peaks in Washington- rainier, baker, Adams, hood, Olympus, and was on the army climbing team on Denali this year, so I think it's safe to say I know what I'm talking about.