I would like to get a prop from each of the Doctors' era. Ones that we quickly associate with that Doctor.
1st Doctor - His cane (I know where to get one, just can't afford it right now) or his ring. (do not own either)
(On all of those I mean replicas of those items if I didn't mention it already. Not really looking to have the actual props and especially the costume pieces.)
2nd Doctor - His recorder. (do not own)
3rd Doctor - I have a replica of his Sonic Screwdriver, but I would really like to get a replica of his Dematerialization Circuit. It represents most of his era more (the whole being grounded bit).
4th Doctor - Big grail item here: his scarf and I have a replica of his 12th season (his 1st season) scarf. I plan to add his last scarf as well. I also have a replica of his sonic.
5th Doctor - I have a replica of his sonic, but it doesn't scream 5th Doctor enough for me. Unfortunately the thing that does the most is his fake celery or his coat. Not really wanting his coat. I'm the wrong body type for it and I don't want it just hanging on display. Plan to add a cricket ball to the display to represent the 5th as well. The one other thing that screams 5th Doctor is his tool box (granted it or a copy was used with the 8th). That or one of his gadgets he had in one of his stories.
6th Doctor - The one thing that stands out the most with this is guy is the same thing I am not thrilled with about this guy... his coat. It's hideous, but you know which Doctor someone is talking about when they mention it. I would probably settle with his Sonic Lance or maybe one of his other gadgets that didn't appear in more than one story. Unfortunately Colin's time was cut short. The only other thing would be to find a umbrella that matches his.
7th Doctor - Well it would definitely have to be his Question Mark Umbrella, which I have. I also have his key (thank you Megatron). The other thing would be his hat which I don't have. It's not easy since I have an 8 1/4 sized hat size. I know it wouldn't be the right size compared to McCoy's, but I would want one to fit my head. McCoy's hat he had from his first episode to his appearance in the movie (okay so the actual hat may have changed but one like it), the same can't be said about his umbrella and key. I do like his jacket though, but it doesn't scream 7th Doctor as much as his umbrella and hat. Oh and the 7th Doctor was the only Doctor to actually keep his hat on most of the time. Tom Baker and Davison would wear them for a little bit and then take them off. TB wore his more than Davison though.
8th Doctor - I have his key (1-800-TREKKER key). I had it before the show aired when they just tried to pass it as the Doctor's key. I have a replica of his sonic screwdriver. Though the two could be mistaken for previous Doctors if someone wasn't up on the props. The only other thing would be his jacket, but I really don't want it either. His console would be nice to have, but it's a bit big.
9th Doctor - Now some don't think much of his costume. I like the understated look after the producers realizing that this might be the way to go. McCoy almost had that except all the question mark motif. I would really like to have the 9th Doctor's jacket. It looks cool and it is something I think of the 9th Doctor when I see it. I would also like to have his sonic, but unless you know the difference between his and 10th's then the two could be mistaken for each other. I am getting some Psychic Paper, but it's been used by three Doctor's now (I don't know if it has changed from Doctor to Doctor or not) though he was the first to use it.
10th Doctor - Not sure what to get to represent him. His sonic has the same problem as the last, but I might go ahead and get his some day because he used it more than 9 (and because I like sonics). I'm the wrong body type for his clothes. I do have some Chucks though. I might get some 3D glasses to go with the his props. The only thing I can think of is that one tracker prop he used in "Partners in Crime"
11th Doctor - One of his bow ties comes to mind first, then his sonic, sonic cane, and his latest overcoat. Honorable mentions: Fez, Stetson, and Top Hat.