5'4 198 eating 1200 is this a good start?

Personally, I would recommend either upping your calorie intake to maybe 1400 or so daily or sticking to 1200 but eating back your workout calories. I say this because for many people, myself included, 1200/day is only manageable for a short period of time. Unless you've got stellar willpower and can maintain 1200/day everyday for months on straight, something a little more manageable for the long term would be a better idea in my opinion. But if 1200/day works for you, stick with it. Everyone's body is different.

So your Mifflin BMR is 1568 (+ or - 5% likely) - which means your body would like to burn 1598 calories daily if you just slept deeply and did nothing else.

You probably burn upwards of 2100 calories without doing any exercise, just doing daily life.

You want to feed it 1200.

And you say you don't want to eat back exercise calories.
So your body burns 400-500 calories purely for mechanical movement during a workout perhaps, and your body is left with 700-800 calories to do a whole lot more than even the 1600 would be providing.
Hope you are not expecting much improvement from the time and energy spent on the workout.

Hope that sounds bad, because it is.

If you really want to lose some weight and don't care that it's muscle mass, here's how to set yourself up for a lifetime of yo-yo dieting by burning off some goods pounds of muscle mass and water weight along with some fat.

Eat that 1200 daily as low carb, 50 g or less.

Do daily intense cardio exercise for 45-60 min as hard as you can, really burn off the glucose and muscle.

You should end up skinny fat in no time, and never have to worry about eating much more than 1200 calories for maintenance, which means you can spend more money from food on say hair care products to care for thinning hair, or other items for rough skin, or bad nails, ect.

If you START at 1200 and then plateau at some point, where do you go from there, cos that's the absolute bare minimum the site recommends. I would start at the 1lb a week figure and take it from there. We all want to lose weight as fast as possible, but doing it in a less restrictive way gives better results long term.

people will tell you its not enough calories - I'm 5'11 and 1200 is working for me just fine - when you get closer to your goals up your calories by 100 every two weeks until you get to a number you can live with.

I'd do pretty much the opposite of this.