Hey, I'm a freshman too in high school! Actually going to boarding school, so I think it's a fairly similar experience to Uni. Fairly. Once again, I'm in no position to offer any advice, but I'll just tell you how I've prioritized things.
1) Getting work done.
That's it. That's the entire list right there. Your number 1 priority is to study. Get work done. That's really the entire point of school; to learn. Unlike the other things on your list, this one determines your life. Literally. If you don't do well/ drop out, you probably won't get a very good job, and we know where that leads. So yeah, study hard, do well, that's your biggest priority.
2) Eating/Bathing/Sleeping
'Sleep is for the weak.' Unless you pulled an all nighter. In that case; 'Sleeping for a week'.
Life necessities. Nuff said. Why do they come after studying? Because you'll probably be going without sleep/ optimal hygiene/ sufficient nourishment when the living hell that is "Exams" come around. Good luck.
3) Socialize/ Extracurriculars
Studying is important, yes, but so is this. All work and no play will make you dull. I grouped these together because with one likely comes the other. Humans are social beings, so be social. Don't do anything you'll regret though. A good way to socialize is to join a club. You'll meet people with similar interests and make friends and such. This is pretty much the "Finding time to keep up with stuff" part too.Kill two birds with one stone. I'd prefer it if they were geese. Geese are evil. Fun times.
4) Romantic stuff
Sorry! This is kinda the back burner imo. It's important. Very important. Just not right now... You shouldn't prioritize this over getting your work done, because that'll get you nowhere in life. I'm not saying you shouldn't have a relationship or look for one, just don't make it your main focus. It'll come in due time, don't rush/force it. And ignore the fact that this is coming from a 14 year old kid who's never been in a relationship but actually gives decent advice I hope. Literally don't know where any of this is coming from. So yeah, all in due time.
In short, each is important. Don't neglect anything important to you, but keep your priorities straight. You'll do fine! Good luck!