It's down to which model you buy from the respective brands. You are going to lose money in the intermediate term for all three, if you buy brand new.
AP, great story, great history, just don't get the useless generic Offshores with too many colour variations...ghost are meant for seasoned and hard core AP collectors.
Rolex Day-date...tried and trusted, but seriously " boring"....but great value, and value retention is best amongst all three. Thus if you want to move on, or give up this hobby, least downside, and secondary market is extremely liquid.
JLC, the Master control series is super robust, and the least "common" amongst the three. But worst resale, and least liquid. Also not that many fakes, unlike the above two. And if any, very bad copies. I hate to say this, but fakes and the increasingly better construction of them is posing a clear and present danger.
Like Nicholas said, think think think......dream dream dream.....if it's a keeper, as it should because of the occasion...it's a family heirloom in the making. Also, in due course you might wanna get matching pair for the missus, should you go down that route...Rolex and AP, easier to get matching ladies. jLC has ladies master control, but small range. Also, there is half a chance that that if you buy the day-date and AP RO, you might even pass it on to your partner, if yours and her view is that the size is acceptable.....and increasingly common view.
Cheers,
Horo