I'm so confused

It's so confusing because everyone has their 2 cents or input when it comes to this. Here's what I've learned through this lifestyle change: not eating them back is not realistic if you want to keep weight off long term. If you haven't been eating them back, you might want to start. You need to be netting around whatever your calorie goal is.

So if my calorie goal is 1800, and I exercise and burn 600+, I should be eating all that back? That seems like an insane amount of food to eat. I barely am able to eat 1400 without exercising.

Yep, eat them back.
Thats why i love cardio days. I can eat pretty much anything without worrying about going over.
Find calorie/nutrient dense food and load up.
EG.
I normally have a protein shake for breakfast after the gym. If i've been running instead of lifting, then i'll ALSO have scrambled eggs on toast for breakfast. Come lunch time i'll have a big meal, and have some nuts/guacamole in the afternoon as snacks.

Congratulations on your loss so far! That's a fantastic progress. WOO WOO!

The calories thing is tough. Based on what you've said here, I don't think you need to worry about eating back ALL of your calories. If you're already eating 1800 a day, and burning 600, you're not going into a huge deficit to worry about. Obviously what you've been doing is working for you, since you're down almost 50 pounds!

I meet with a nutrition counselor who has me on 1700 a day, working out with cardio 3-4 times per week, 60 minutes each and 2 weight training a week. She said not to eat back the calories. I'm sticking with that, and so far it works when I follow her guidelines.

Welcome to the club... This is one of those "chicken vs. egg" type debates, both sides have good information, and both sides have valid points, and both sides will tell you why the other way is horrible.

In *MY* opinion, it depends on how you calculate your calorie goal. For an example, I am going to use the Harris Benedict Equation to help explain the numbers.

According to that equation you start with your Base Metabolic Rate (BMR) which is calculated as follows:

Women: BMR = 655 + ( 4.35 x weight in pounds ) + ( 4.7 x height in inches ) - ( 4.7 x age in years )
Men: BMR = 66 + ( 6.23 x weight in pounds ) + ( 12.7 x height in inches ) - ( 6.8 x age in year )

Then you determine your activity level:
Sedentary = little or no exercise
Lightly Active = light exercise/sports 1-3 days/week
Moderatetely Active = moderate exercise/sports 3-5 days/week
Very Active = hard exercise/sports 6-7 days a week
Extra Active = very hard exercise/sports & physical job or 2x training

To calculate your daily calorie goal you use the following:
Sedentary = BMR x 1.2
Lightly active = BMR x 1.375
Moderatetely active = BMR x 1.55
Very active = BMR x 1.725
Extra active = BMR x 1.9

So, again, as an example. I am a 155lb, 5'3", 24 y/o female. My BMR is 1,513 calories per day. I have a desk job, and exercise 3 times per week... most weeks...

So, to calculate my caloric need I have 2 options:
Sedentary = 1513 x 1.2 = 1,816
Lightly active = 1513 x 1.375 = 2,080

Depending on my choice, I will determine if I eat back my calories or not. I am "lightly active" but not ALL the time... So, for me, I would choose the Sedentary total of ~1,800 calories per day, and when I exercise I will eat them back.

BUT, if I ever got to the point where I KNOW I'm going to exercise those 3x per week, I'd probably switch to the Lightly Active choice, and NOT eat back my calories, because that burn is factored into my daily goal.

Don't know if that will make it less confusing or not, but that's the way I make sense of it all.

That sounds like a solid approach. As for the HRM, personally I love the Polar brand. I had an FT4 and now have an FT60-- The more you pay, the more features you get, the accuracy is the same for both. If I buy another I'll get an FT4 again, it's about $100 and well worth the price. I lost 50% of my overall goal using one before I joined MFP.