Hellloooo,
I agree... this health and fitness stuff can be very confusing... and frustrating when one person tells you one thing and another immediately tells you another.
If you want flat abs... you MUST watch your diet and stick to a regular exercise routine that includes weights and cardio. In my opinion, the most important thing is diet because you can lift weights all you want but if you're not getting enough protein, watching your calories, and fueling your body properly you will not get as much out of your weights and cardio. Ab exercises such as sit ups will work (to a small point) to build up those ab muscles, however, yes, as you said unless you lose the fat off the ab muscles your work there will not be visable. It really kills me when i see people lay down and crank out 50-100 sit ups... and expect that one thing to get them a flat stomach. The truth is they would be better off doing a full body strength routine, which would work ALL of their muscles including their abs as this would burn more calories, help to work all muscles (which has a wide variety of benefits including injury prevention), and build an overall better looking physique (in my opinion).
As for the free weights v machines question... I personally prefer free weights, however I do occasionally use a machine to switch things up. The machines are great because you are less likley to drop the weight on yourself if you're pushing heavy and it forces you to use proper form. If you're just starting out and have no idea what to do with free weights the machines are definitely an option until you can get some help in the free weight section (have you thought of hiring a personal trainer for a week or so to get you started?). I prefer the free weight as it forces me to have full control over the weights so not only do my muscles have to lift, but they also have to stabilize... basically getting more bang for the buck. However, as i said, there are times when i do use the machines just to switch things up.
One thing to keep in mind.. this exercise and diet stuff goes sooooo farrrrr beyond just making you look good. There are countless other benefits that come with exercise and a proper diet: They can extend your life, help to prevent diseases, reduce depression, anxiety, and stress, and make you look better which ulimately can improve your self esteem which can improve many other areas of your life.
Hope this helps. Feel free to ask questions if you have any.
Cassie