What is the best work out routine as far as days off and days on

It depends on the exercise. Keep in mind that the day off is a "rest" period. This is when the muscles that were exercised the day before, repair and recuperate. Every "body" reacts differently generally based on diet, nutrition and age to name a few. Intensity is another.
If you did a biceps routine 2 workouts in a row with a rest day that would mean the muscle had 48 hours to recoup. Please... that is just an example. I never design programs for my clients with the same exercise in consecutive workouts. FIND A GOOD PERSONAL TRAINER.
Sorry... didn't mean to shout but you are talking about developing a lifestyle that hopefully you will stick with the rest of your life. It will determine your overall health, your mental attitude, your ability to relate to others, how well you do your job and so many other facets of life. That is worth investing in.
Its like a college education... you get to keep what you buy for the rest of your life. A good personal trainer is like a good professor. They may not have an MA or a PHD, but did they TEACH you what you came to learn. You may have to try a few before you find one that you feel "right" with. Remember, o good personal trainer must be a good communicator and a good teacher. If you go into a session with a personal trainer and he/she stands there with a clipboard and "counts" your reps--RUN AWAY. That is what I call a "rep counter" and no matter how many degrees of certifications they may have---they're not teaching you. A good personal trainer teaches you that counting your own reps is a key building block of your entire exercise education. Your rep count should control your breathing and the pace of the exercise. Without those 2 things--- you are "off the tracks" and will never have a successful exercise program.

It totally depends on what your goals are. If you want to be generally fit and strong, then I'd suggest three days a week in the gym, doing a total body workout, concentrating on exercises like squat, deadlift, bench press, military press, dips, pull-ups, stiffleg deadlifts.

On non-gym days, do cardio. Work hard, you should be sweating and puffing to get results. On at least one day a week, and possibly more, depending on your fitness level, have a rest day when you can do ordinary activity like walking and dancing but not intense cardio or heavy weights.