If the old domain AND I'M NOT SAYING IT WAS!, was penalized for shady practice, seriously bad coding, bad neighborhood, other black hat and this move to new domain is in hopes of starting over, then I would not redirect from old to new, nor would I move pages (as they exist) from old to new.
The negative can also happen by poor advice, out-dated seo tricks, or other past practice which, these days, will knock a site out of the serps. AGAIN, I AM NOT SUGGESTING this is the case.
If you are starting over to get a clean slate and another shot at ranking in the serps, then make a clean break, rewrite the content that has value (and vet it, make sure it is unique, or at least original). Same goes with images, unless they are so generic they can't be tracked all that well.
The major se's have long memories, they never forget, they follow whois, and there's few places to hide, and their repository of past sites/pages is immense, and GROWING, as well as their ability to comb through that mountain of data and make comparisons.
I've had several clients over the years who did combinations of all the above to some degree, a few by intent, the rest by accident, and the clean break, new whois, new dns, new everything, including the content, followed by best practices managed to save their companies or business endeavors for on line presence and enterprise.
I DO NOT IMPLY the OP engaged in any of these activities! Just mentioning that should any of the above apply, and was not a one off accident quickly remedied (and usually forgiven by the se's) don't make a move to recover unless there's a clean break, else you'll be caught out and whacked a second time, perhaps even harder.