Does your saxophone have sticking keys that make it difficult to play?
The first point would be to not eat or drink before or while you play saxophone. Water should be the saxophone player’s beverage of choice when you’re playing or are about to play.
In terms of cleaning it, don’t buy a synthetic fuzzy saxophone swab-stick!
I had one myself, but then I cut off the cap and threw it away. They work somewhat well at first and are convenient.
BUT as they age, the fibers come off and get stuck to your saxophone’s pads. These fibers then create micro leaks which can hurt your sound.
Some saxophone players have used them for years and think that they work wonderfully. However, I know of problems they have caused. If you go to a repair shop and they have a special light, it can reveal the micro leaks in the horn.
It takes a little more time, but get a swab with a string that you run through the saxophone. I have a one for the body and one for the neck and mouthpiece.
Personally, I clean my saxophone each time after I use it. My cleaning consists of running the body swab through twice and then cleaning the pads on the spoon keys as well as swabbing the neck and mouthpiece. Some players almost never clean their horns.