Welcome Alex!
Good to see you've set yourself some training goals! Just want to chime in with a bit of advice, since you asked.
First of all, don't try to ride three horses with one ass, especially during the novice linear progression. Once you get your squat up into the +120 kgs range (and you will, if you run this well), you won't feel the need for badminton as cardio. If it's something you do because you enjoy it, don't go crazy with it. You'd be amazed what properly performed squats, presses, and deadlifts under load will do for your overall flexibility and mobility. Again, if yoga is something you already do and enjoy, don't go crazy with it. Commit yourself running the best LP you can run for at least 12 weeks, and that means making strength acquisition the top priority, preferably to the exclusion of other goals you may have long term.
Next, those are very conservative starting numbers. My dad started at 68 with absolutely no training history, and he started off squatting 65 lbs, pressing the empty bar, deadlifting 95 lbs, and benching 65 lbs, and made some 5-10 lbs jumps for the first few weeks. If you're feeling comfortable with the lifts now, take a couple of workouts to select starting weights as described in the book and don't be afraid to be more aggressive. A lot more aggressive with the deadlift in particular. Remember, you're more likely to hurt yourself playing badminton than strength training. If you're not comfortable, post some videos either here or in the technique forum and we'd be happy to help you improve your form. If you insist on being super conservative (and some do, for some reason), you'll have to give yourself a lot longer than 12 weeks to reap the benefits of the program.
Finally, the SSNLP is not a weight loss program. You didn't mention your height, but 205 lbs and 20% BF hardly makes you a fat slob. It's possible to pull off some body recomposition, with the scale staying the same, or even going up, while your waist goes down. Focus on the weight on the bar, not the weight on the scale, and track your waist circumference if you want to feel good about losing some body fat. 200 g of protein per day, lowish fat, and lots of carbs while you get stronger will do wonders for your appearance and performance under the bar. However, this also assumes you're challenging yourself appropriately. I suspect you could be moving more weight, even with no lifting history, which will give your body something productive to do with all the extra protein and carbs. For more detail, go have a chat with Santana in the nutrition forum. He's a fantastic resource.
Hope some of this was helpful! I look forward to following your progress.
Happy lifting!