Records and letters, in my experience, are more doing-motions-to-move than actually doing anything. In general, nobody cares if you had a spotless record, or were employee-of-the-interval unless it's a well-known company, in a highly visible situation. Many of these things are simply expected, so long as you present yourself as a level-headed individual that can GTD. At best, they're a conversation point at some point in, before, or after, the interview.
Once you're no longer in the employ of a company, it's more or less a done deal, especially in terms of a layoff. Next year's taxes are about the only thing that matter here on a long-term basis, and if they've been paying to UI (legally, they should have been).
Mark the point of employment on your personal permanent record (read: your resume/CV/online presence) and talk yourself up a bit in terms of what you've done with honesty. That's one of the hardest parts when you've been freshly laid off.
In the immediate future, what needs to happen is ensuring continuity by making sure that you have your UI filed with the state and ready to be processed, while looking for that next place. They tend to ask if you've been looking for work, and you will have to show proof if they ask. The cushion, while it lasts, tends to be helpful in such a time.