How to get better at calisthenic workout for beginners

I'm 22, 5'7, and weigh 138 lbs. I've talked to many people giving me advices about increasing reps for basic calisthenics, and the only one I follow is "Just do them." I'm good on cardio, but when it comes to calisthenics I suck so bad. I've gotten mixed advice and both seems play for me, but then I don't know which to follow. One said to build some muscles by lifting weights, while the other says avoid weights and just go with calisthenics. I want to be able to do more reps for sit-ups, push-ups, and pull-ups, but I don't see myself improving much at all. I don't really have a workout routine. I'm in the navy for less than 6 months and honestly I feel ashamed that I can only meet the minimum physical requirements to pass. I want to be able to go beyond that and better my physical shape. I've noticed that I have a weak lower core because I get tired doing sit-ups at 30-40 while others are still going at it. If anyone here is or was on the same boat as me, any helpful advice? What was your workout routine like when you first started? What was your diet like? Any useful advice would be much appreciated! Thanks in advance!

Also feel free to add me, I could use the motivation!