26, looking to drop 20lbs

Hey, joined the site a week or two ago to keep track of daily calorie intake. I currently weigh 196lbs and am 6' tall. My wife and I are headed to Mexico in 10 weeks and I'd say to get rid of my 'excess' for the trip I'm looking at dropping about 20lbs. 

I've done a couple of "calorie expenditure" calculators and with my sedentary lifestyle (office job) I need about 2500 calories/day to maintain my current weight, so I've started targeting approx. 1500-1800 calories/day for the past 4-5 days.

I also started back to the gym last week, twice a week for approx. 10-15 minutes of cardio as a warmup leading into about 45 minutes of weights. I'm sore haha. I figure I'm burning about 500-600 calories while at the gym since I typically burn about 100-150 in the first 10-15 minutes.

So with about 700-1000 calories less per day than my 'maintain' intake, plus an extra 1000-1200 or so burned at the gym every week, I should be looking at losing my target 20lbs in about 9-10 weeks, which is pretty much in line with the recommended 2lbs/week... and just in time for our trip.