So you've gone back in time....

I'd take the machine to the late 70s/early 80s and scoop up vintage punk/hardcore/post-punk/industrial/etc. vinyl/zines/tapes that would cost me major $$$$ on eBay today. Maybe catch some shoes at CBGB's, Mabuhay Gardens, Mudd Club, and the Masque as well.
And tell Anya Phillips to have that lump behind her ear looked at ASAFP.

Technically he can't kill him lest he ceases to exist. If his grandfather is dead then he is never born meaning his grandfather lives and so does he.

Travel to the future to kill your future self before you have the chance to travel back in time so that you can never go back and kill your grandfather and thus saving yourself from creating the new reality timeline that would cause you to not exist... in that new timeline.

Travel back in time one minute and then take your past self and travel back in time with them and repeat.

Soon you will have an army of you and can take over the world.

but then you would have removed yourself from the timeline before you reached the time machine making it impossible to remove yourself from the timeline

You are forgetting that by traveling back in time you would create a new timeline, one in which has no effect on the timeline you left.

Eh, if I went back to Renaissance, I'd gather a blunderbuss, some of the finest liquor available and sit outside a castle and yell about how those tight wearing pansies should keep off my lawn/moat/whatever

Then possibly come to power with nothing more than a lighter. and try to take over Turkey for it's tobacco.

You're going to have to go back one minute, then two and then three because you've already taken your past self from the one minute timeline.

You keep thinking that you end up in the past of the timeline that you left, but it is doubtful that would be the case. So you would be taking yourselves' from the one minute ago time from multiple timelines. Once you leave your own timeline chances are you could never get back to it. So whatever you did in the new timeline you find yourself in would have no effect on the timeline you left.

That's creating whole new dimensions. Does the time machine cross over dimensions or stay on the one you have lived on? I don't see how it is possible to grab yourself from a plane of existence you had nothing to do with.

So in order for the universe to avoid a paradox, a new timeline if forged simply by the act of you traveling back in time.

So that's your interpretation and mine is the opposite

You're speaking to someone who gets quantum physics but believes a lot of it to be codswallop so we could be here all day debating.