The only of the options you list that would not be a blatant lie are "supported by family" and "unemployed". Lying can emphatically not be recommended -- that will make it somewhere between very hard and impossible to qualify for a visa ever.
It may sound like you can squeeze in under "supported by spouse/partner/other", but that would not really be an advantage for you. They're going to look closely at your particular circumstances no matter which box you check, so what your goal needs to be is not to micro-optimize which box you think gives a slightly higher chance, but to avoid them thinking you're trying to hide something. They hate dishonesty much more than just about any truth you could possibly tell.
Yes, as a young person with a fresh education and no job, there's a definite risk that the ECO will think it could be attractive for you to stay in the UK illegally to seek work. You can't escape that suspicion by tactical answers to the application questions. What you need to do is convince them that it is more advantageous for you to return home than to abscond and stay illegally. How to do that depends entirely on what makes that advantageous to you -- if your family is well off and your education is one that gives you a good shoot at a nice legal job in your home country, things will go much smoother than if you're dirt poor with no prospects locally.
If you can't lift that documentary burden, you probably won't be going. Wait until you're more settled in your life instead.
Note that it probably will raise eyebrows that you're apparently proposing a family vacation in the UK lasting only 2 days. You don't write where you're from, but since the UK's nearest neighbors are all EU members whose citizens don't need visa, I suppose you're so far away that the hassle and cost of traveling to the UK would hardly be worth it for only a couple of days.
A suspicious ECO (and they're paid to be suspicious) might get the idea that the entire family is only proposing the vacation as a pretext for getting the son/daughter into the UK to get a chance at a better life, and that 2 days were all they could convincingly budget for.