644 is pushing it a bit, though it really depends which card you're applying for. AmEx usually extends credit to those with 'good' (650-750) to 'excellent' (750-850) credit scores. If you don't really care which card you get, I'd stick with either the Clear or, if you have a Costco membership, the True Earnings. Those two cards are for the 'good' credit range.
The True Earnings card actually takes into consideration your purchase history at Costco so that may help you or hurt based on how long you've been a member, if you are one. You may even consider signing up for a Costco membership and apply for the card when you sign up -- you mentioned needing to buy stuff for around the house and Costco has great prices on all sorts of household stuff.
Also, if you have had or already do have an account with AmEx and your record is relatively good it'll improve your chances of being approved. It might be worth it to wait a couple of months before applying though.