I've actually had the thought cross my mind about time travel and picking heh.
Personally speaking I would go back in time and collect old signs as those seem to be in high demand. Old photographs, autographs, old toys.
I would buy these things brand new and to ensure that there is a marked passing of time I would get some type of shelter or cellar. Because if I can time travel why not use time travel to make a fine fortune?
Use that fortune to make a memorabilia cellar. And in this cellar I would stockpile massive amounts of things.
It has come to my mind that if you buy something new and take it to the future new then buyers will scrutinize it and there is a chance they will consider it a very fine forgery. But if it actually sits in a basement collecting dust for 40 or 50 years then it's authentic.
In addition to what I listed above perhaps things from the atomic age, when people were selling highly dangerous machines with unprotected x-rays and radium tonics. Memorabilia from the cold war. I'd get my hands on nearly everything Elvis related, not that I'm a fan but just to sell off to preservation societies. Maybe take a smartphone back in time and take video of the king?

Stockpile old movies, get my hands on recordings that have been lost time and carelessness and make hundreds of redundant back up copies of things. Old movies that will never be seen again, the original broadcasts of the old Doctor Who.
Just keep it in my bunker and sell it all off slowly and gradually, auction it off to the highest bidders.
Just imagine Mike and Frank coming to me and finding out I have film reels of movies that were thought to be forever lost in cinema fires.

"You wanna buy this? Well seeing as it's pricless and all and the only one of its kind I think I could let it go for.. say. Five million dollars?"