Your push-ups, pull-ups, sit-ups and running are great. With those numbers you shouldn’t have any problems. As you know there will be much more drills and evolutions involved in your basic training, but I think you are in a good place as far as your upper body strength and running goes.
For rucking, get a backpack and put in about 50lbs of weight (40lbs if you haven’t’ done any rucking before and bricks would be my first choice) and go for longs walks at least 4-5 days/weak. Chose all type of terrain (including water, hills, dirt roads, sand and concrete) and start walking. It will be some discomfort in the first few days (especially in your upper and lower back and feet), but it will be a good conditioning training for you. Take good care of your feet because you don’t want to get blisters that will make your basic training a painful experience. When wearing boots, use thick and dry socks as much as you can and make sure you have the right type of boots (you can start with athletic shoes and slowly switch to army boots). If you need more tips/help please feel free to email me. Four weeks out is not that much time to get your rucking conditioning to optimal levels, but it will do for basic army boot camp training.