Well you're more then welcome. Thanks for taking the time to read the thread.
I have a couple of random thoughts:
1. You ask if this is the "right way." There is no right/wrong when it comes to this. What's right is a method of doing things that works for you in such a way that a) it provides you with the results you're looking for, b) is maintainable for life, and c) doesn't cause you a lot of grief - preferably you enjoy what you're doing.
2. A fat loss plan is quite simple. It's when you start programming for someone who wants to increase strength/power, has an injury to consider, has a few imbalances, wants to cut a little fat, and needs to peak for a big competition in three months that "personal training" gets hard.
The way I look at fat loss is this:
a) pick your calorie goal. This should never be a complex issue as your calorie needs are going to change with time based on your weight, activity etc. The first step is determining your maintenance, which is not BMR. Maintenance is BMR + activity + digestion of food.
There are many ways of finding your maintenance but a good ball park is 14 calories per pound of bodyweight.
b) from there, create a deficit. I like the idea of eating as much food as possible while still losing weight. That seems to be the most sustainable approach for a lifetime. Something like a 20-30% deficit from the above calculated maintenance is a good starting point. You're current intake of 1550 puts you at approximately a 30% deficit so that's good.
c) Track your progress and respond according to feedback. If things aren't heading in the right direction, it's really no reason to get worked up. Simply troubleshoot the issue and take advantage of those around you, including people on this very forum. The cool thing about this that some people tend to forget is this process is very flexible. If something isn't working within 2-4 weeks time... it's not like we invested a ton of time and money into an impossible task. We simply have to be light on our feet and willing to roll with the punches.
d) Once a caloric goal is decided, we need to be sure to account for nutritional value of the foods that comprise said calories. Nutritional quality goes a long way in health, preservation of muscle, hormonal factors that regulate metabolism, satiety, etc. Be sure to think of more than just calories. I'm sure you know this already but it's worth mentioning.
A lot has been discussed here in the stickies about nutritional quality but if you want elaboration, simply ask.
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The above calorie range factors in exercise. It's assuming you're moderately active with exercise. So lifting some weights and doing some cardio is a good idea.
Weights add to your caloric expenditure. More importantly, it stimulates muscle maintenance which is what gives us the shape and leanness that many of us are shooting for.
Cardio buffers the calorie deficit. Without it, you are forced into eating less food.
Both weight training and cardio obviously have other positive influences such as health, strength, performance, etc.
The application of weight lifting and cadio is another topic unto itself as how to apply each to your given situation depends on your experience, your exact goals, your body, etc.
I feel like I'm throwing a lot of generalities your way without answering your questions... I simply want to be sure you grasp the "foundation" before throwing the walls up.
Should I continually eat slightly above or at that caloric intake and just exercise my way through weight loss?
That intake, with exercise factored in, should provide you the deficit required to realize weight loss. I don't like that term, weight loss. I much prefer fat loss as each have very unique differentiations that are quite powerful.
Is this the correct way? I don't want to be unhealthy and I don't want to starve myself in a drastic measure. I dunno, I just need a little clarification
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You're certainly not starving yourself. That said, it's hard to determine the health status of a plan based solely on calories. The nutritional quality of the foods comprising said calories is critical.
