Don’t worry too much about where you start with your daily nutrition, it’s more about the adjustments that you make than the starting point. I think people spend way too much time trying to calculate their BMR and figuring out how many calories they need. If you’re wanting to start at 2,000 calories that would be fine; now you just need to decide how to distribute those calories amongst your macros.
If you’re at 200 p and 200 c, that means you’re only at 44 g of fat, which I think is a little low. You could consider dropping your protein to 1.25 g/lb bw, which would put you at 180 g a day and free up 80 calories to assign to fat. Just stick with these numbers for a couple weeks and let the scale and mirror be the judge of where the numbers need to go.
As a beginner, you can be a little more loose with your weight gain initially, but I’d caution you against getting in the mindset of thinking you just need to gain weight. Simply consuming a large surplus of calories and gaining weight doesn’t mean you’re building muscle. I would shoot for about 2-3 lbs gained per month; it doesn’t seem like a lot initially, but if you kept that up for a year you’d have added around 30 lbs. That would be a totally new physique for you. I’d monitor your weight gain, and if you don’t gain in a given week, bumping up carbs by 10-15 g and fat by 5 g every other week would be a good place to start as far as adjustments.
You mentioned that you drop carbs significantly on off days. You’ll get lots of different opinions on this, but I personally am not big on reducing carbs on rest days, at least not cutting them in half as you’re doing. Your body still needs nutrients to grow on these off days, and depending on how many days a week you’re taking off, I would think that cutting your calories significantly on multiple days a week could inhibit your ability to ramp up your metabolism. Of course, that could be similar to carb cycling, but I don’t think you’re at the stage where you need to get that specific with day to day changes.
Hope that gives you a few ideas man!