I flew P-3 Orions. When I applied to the Navy, I was lucky- they needed pilots. The Navy had cut pilot slots too far and they had a deficit of pilots when I applied. Had they been fat on pilots I doubt I would have gotten in- my college grades were terrible. As far as competitiveness, one thing you have to get used to from the get go is that you're going to be competing from day 1 if your goal is to fly, and continue to fly, jets.
When you get to OCS, you'll already have a pilot or NFO slot, so there's no competition on that score. Once you get accepted to OCS, unless you're a total flake, getting to Pensacola should be almost guaranteed. A few folks got clipped by medical- you can pass all the physicals you want before OCS, but the one they give you AT OCS is the one that counts. They are very, very thorough and absolutely ruthless in dropping you from aviation if you don't pass the physical. I got popped twice- once for my vision even though I was 20/20 in my pre-OCS physical, and a few times for my height. I got re-tested on vision and passed. I also got measured about 30 different ways and barely, I mean exactly, passed the height requirements (almost lost on the knee to butt measurement). One woman who was the same height as me didn't pass that length test and was dropped. Another guy had some heart murmur or sound or something that was enough that they dropped him. The woman DOR'd, the guy changed to intel.
When I reported to flight school, I got measured again. Basically they put me in a cockpit of each plane in training (man, that T-2 fit like a glove!) and then made me touch all the buttons and stuff. I couldn't full deflect the rudders in the T-44 so I fudged it by scooting forward a bit and saying I could get full deflection when I couldn't. In the T-34, they put a helmet bag 50 feet in front of the plane and you had to be able to see it from the cockpit. Of course I couldn't see it, but I said I could

When I eventually got assigned to P-3s and had to fly T-44s in training I used to fly with my NATOPS manual behind my back to scoot me forward enough in the seat to fully push the rudder pedals.
Once you get to flight school, it is very competitive. In order to qualify to select jets, you have to have 'jet grades'. When you do a flight in primary flight school, you get graded afterwards on 20 or 30 criteria, below average, average, or above average. A good flight will net you a single above average (or one more above than below), a great flight is two aboves. Over all the flights you add up all your aboves (think of it like a K/D ratio) and they average all the aboves for the last 90 guys to graduate. Say the average number of aboves for a graduating pilot is 30. To qualify for jets you have to be in the top 50%- so you'd have to have 31+. If you have 30 or less, you have to select from other platforms than jets (P-3, E-2, helos). Right from the beginning, then, you are competing for a 50/50 chance to even ask for jets.
Say you graduate, and you have jet grades, say 37 aboves. Then they take all the guys graduating that week from all the training squadrons and compare those guys against each other. Say there's 4 guys graduating that week with jet grades. There are two jet slots available that week. Well, they go to the guy with the highest average and see what his first choice is. If it's jets, he gets them. Then they go to #2. He wants jets, he gets them. #3 wants jets, but all the jet slots are taken. He gets his second choice. #4 wants jets, but they're taken. He wants P-3s second, but they're taken. There are no E-2 slots that week. So #4 (and anyone below him) goes helos, even if he was way above average.
This is sort of what happened to me. I graduated #1 in Corpus Christi my week, but there were no jet slots at all available so I got my #2 choice by default. Some weeks everyone got jets, some weeks nobody got jets. So, it's competitive, but then the needs of the Navy always take precedence.
Ok, so say you got P-3s. You go to advanced flight training and it starts all over again. You have your heart set on being detailed to a P-3 squadron in Jacksonville. So, you go through advanced and then they rank everyone against each other and they assign squadrons based on what you want based on your rank. The first guy gets what he wants, the last guy gets whatever's left, and the middle guys fall out somewhere in between.
Ok, now you report to your squadron. Well, every year you get a fitness report- like a report card on your performance. You're ranked against everyone in your squadron in the same paygrade. You can get a promotable, must promote, or early promote (best). But, only 10% of the people ranked can get an EP. So, you're competing against your peers from day 1 to be ranked in that top 10%. When it comes time for orders, the detailer is going to look at what you want, and how you're ranked against your peers and that will determine where you go.
When it comes time for promotion above O-3, your file goes in front of a promotion board. There they look at your total fitness reports and compare them to everyone in the Navy in your paygrade (this is simplified a bit, there's other factors like type of duty, etc. that factor in). If they can promote 50% of the Lieutenants then you get ranked and promoted if you're in the top 50%....
So, are you starting to see a pattern here? From day 1 you'll be competing for everything in the military. You're always being compared to your peers. Some of it is politics, some of it is being the 'favorite' and some of it (not much in P-3s unfortunately) is just plain being good at your job. My strategy has always been to just do as well as I can and let everything fall out where it does.