Better is always the enemy of good enough. If you hold out forever waiting for 'better' to come along you might end up with nothing.
So, if you decide to go for the first one, stick with it, tough it out and make it count. Remember that if you are looking for long term relationships that there always will be a better. Then when something much better comes along (not just a bit better) make your move with proper notice given.
I know it's a dog-eat-dog culture out there, but especially in the current climate a reference (a good one) can make all the difference between getting the next gig or being on the dole.
This goes against the grain, no doubt, but I've found that in the long term the more ethical people come out on top. After all, there are only so many bridges you can burn, a CV with a bunch of holes in it does not look very good and it is a smaller world than you probably think it is.
If and when a much better offer comes along you can always give your current employer the chance to match it. That way if they can't match it they will know that they lost to a party they could not outbid, they're not going to blame you for moving up. But they will blame you for not showing up when you first accept. After all, what's to stop you from doing that again and again ?