In fairness, I apologise my reply was a bit over the top. It's just irritating to see the same sort of questions over and over, but I will concede that I acted like an arsehole. So I am sorry for that.
The point is you need to do the research yourself and I should have said that...
Anyway, as for TC 16610 - It doesn't exist anymore. TC is long gone. There are rumours in which you could google... and see where they lead you to a certain watch brand beginning with G.
Right now if you're after a 5 digit rep you're looking at JF no rehaut engraving LN/LV. Or the more recent and newly added ARF.
https://puretimewatch.io/watch-bran...rf1-1-best-edition-on-ss-bracelet-sh3135.html
This is the one you should go for, it will need a new date wheel (genuine) + crystal to be almost perfect. But out of the box is fine too, just a little fat on the date wheel.
The search function of the forum isn't quite working properly, so I will help you. But try and go on the appropriate subforums... ie Rolex board and look for threads. You can find heaps and heaps of information on each watch and people go into great detail on flaws and what requires work, what to look out for etc.
Good luck and you're right, when you're new it is a minefield, there is an overload of information. But take your time, learn and you will do well. Sorry for my initial response.