I know there are many that are fans of him here, but I would stay far away from Goggins, unless you feel like injuring yourself. He has a very unhealthy relationship with physical activity.

You got 13 months, that is easily doable for what you are wanting to do. Most important thing for running is just to slowly build a base. Start off running 2-3 times a week. Maybe just try to run/walk a mile each time. Keep your running pace relatively slow when you are starting out. The goal is just to build up your aerobic base. Get to a point where you aren't having to walk to complete a full mile, then start slowly increasing distance. I'd say working your way up to running a 5k should be your goal, although you can certainly work past that if you'd like.

When you are able to maintain running for longer than a mile without having to take walking breaks, start focusing on speed. So maybe once every week do a run where your only focus is maintaining a pace that will get you to comfortably pass the time requirement (like a 10:00 min/mi pace). Start with some intervals, maybe 3 intervals for 200 meters at that pace, with walking in between, and then just continue to increase distance and number of intervals.

There are also "couch to 5k" programs you can follow that will likely get you to where you want to be.

Some continued weight loss is really going to help with endurance and injury prevention, as well, so keep at it.

As for weight training, you can sometimes find cheap weight sets on Facebook marketplace, but weight sets aren't 100% necessary for resistance training. Focus on progressive overload with resistance training, meaning continued increase in either resistance or reps each set. For example, if currently you can only do 5 push-ups for 3 sets, your goal for your next workout session is to do 6 push-ups x3. Once you can do 6, do 7, and so on. Do the same thing for sit-ups and every other workout indefinitely.

Your workouts are going to be a bit limited due to lack of free weights, but not impossible, you can look on places like Reddit for additional ideas. Exercises like bodyweight tricep bench dips, body weight squats, lunges, planks, bodyweight row, various sit up and push up variations, can be done, but as your fitness improves, you will start to get limited on your gains unless you are able to incorporate free weights or gym equipment.

As for diet, don't forget the importance of adequate protein intake. If you are wanting to put on some muscle, optimal protein intake is going to be 1.2-1.6g of protein/kg bodyweight. Also, you don't need to demonize carbs, but recognize that carb heavy foods are typically less satiating. There are going to be varying opinions on how to appropriately lose weight via diet. I've seen a lot of push back, online at least, with calorie counting due to the risks of developing disordered eating from calorie counting obsession, but IMO, some form of calorie counting is going to be the only way to reliably and reproducibly lose weight if not on GLP-1 agonists.

The first step with calorie counting is finding out what your TDEE (total daily energy expenditure) and BMR (basal metabolic rate) are. TDEE is going to be your total estimated number of calories burned on average per day, so it's important you answer honestly and maybe even slightly underestimate your daily activity when calculating on these online calculators. Your BMR is going to be the amount of calories you burned if you did nothing all day. There are plenty of online calculators to give you a rough estimate of each. 1 lb of fat loss requires roughly a 3500 calorie deficit. That means if you want to lose 1lb a week, you need to average 500 cal deficit per day. Make sure to be honest with yourself when evaluating serving sizes when adding up your calories, and again, I tend to round up slightly so that I am always ever so slightly overestimating my calorie consumption when in weight loss mode. As you lose weight, you will need to recalculate your TDEE and BMR if you are wanting to continue to lose weight.

Good luck on your journey!