Newbie Help: Datejust 1603

[mkskate9]

I hope I put this in the right place, if not my apologies. First time poster here.

I am fairly new to collecting and am looking for a bit of advice and direction. I am interested in picking up a vintage 1601/1603 Datejust with a grey dial. I found a few offered by beckertime. From what I have read here, they have some mixed reviews and the general advice to is use your own judgement and read their descriptions before buying from them. That being said, before I send them anything on a trade and part with my hard earned money.

beckertime. com/product/used-rolex-datejust-mens-3733695mt/
beckertime. com/product/used-rolex-datejust-mens-7333391nmt/
beckertime. com/product/used-rolex-datejust-mens-dj641111mt/

At least to my novice eye, everything looks alright, despite them being unable to send photos of the movement. Although, the hands in the first link almost look too new compared to the lime plots? Anyway, thats why I am asking for the help of some experts here! Let me know your thoughts.