The best way to quit is to stay on good terms with your current employer (in case you need them as a reference), and look for another job while still working for them. Once you find another job that you want, and you've been given a start date, then give notice at the old job.
I guess I'm confused though, because it sounds as if you currently have 3 jobs? Or are you working one and being offered two others?
If you're still young, and depending on the type of work, having to work shifts you don't want is necessary at times. I had a few different jobs when I was young where I had to work evenings and weekends, and one at which I had to work graveyard shift.
Every employer is different as to how they handle shift work. Some like people on "permanent" shifts - which might change if the person changes tasks or gets promoted but are otherwise static. Other places have rotating shifts. There's usually a more preferred shift that most people want, and usually those with the least time on the job get the least desirable shifts, although sometimes there's a senior employee who likes the odd shifts. When you've been employed for a while and openings come up on better shifts you may get a chance to move to a better shift.
If you wind up on a shift you don't like, I would always make sure your boss knows that you want to be on the waiting list for another shift. (Mind, you might be behind a few others on that waiting list.) If there's a high turnover and you do good work, it might be sooner than you think to get a better shift.
If you have to train people or are a lead on the shift you're on, make sure you train the others well enough that they can be relied on to take over if you get the chance for another shift. Give them a chance to get to know one task really well, and then another, and another, until they know everything you do. This also keeps their job interesting for them, so they'll be more interested and likely to do a good job. On the other hand, if you just give them the grunt work, they'll get bored or disinterested and won't learn to fill your shoes. Then you could be stuck there longer. This can be a win-win or lose-lose situation, and you might have more control over it than you think.
It's also a good idea to take your employer up on any training they offer. Not only does it open up new opportunities for you because you'll have more knowledge, it also lets management know you're eager to learn and interested in the company. That's the kind of person they look for to promote.