Personally I would go for the Chase Sapphire Preferred. Spending another $1000 in three months should be an easy thing to do without having to spend more than your normally would. Gas and groceries with a few additional purchases (eating out, clothes, home goods, etc.) would easily get you there I think. But, if you think you're going to be prone to spending more than you would otherwise, I would probably reconsider getting a credit card at all.
I don't think that the 0% APR for 12 months should be considered in this situation. That's much too short of a time frame to think about investing instead.
You already said you'd be prone to spend more than normal to hit that $4k for the Chase. Seems it would be just as easy to say, "I can buy this stuff now and I don't have to pay for it for a whole year!"
It takes a ton of discipline to sign up for credit cards purely for sign up bonuses and cash back rewards. The credit card companies can offer such good bonuses because they know the vast majority of people are going to rack up way more in interest and debt than they'll ever pay in bonuses.