Laminator - you're going to have trouble applying a selfwound adhesive on an application table (unless there is a trick that I've missed), as I believe they are designed for laying down self adhesive materials to substrate (mainly Vinyls, cut or printed). And as you'll be working at the nip, the best chance of getting to dust spotlets, before they meet the adhesive, or worse, the print.
But, as you have no constraints on cost or space, go for both, but upgrade the laminator to one with a heated top roller, so, should you choose to laminate the images, you can be silvering-free from the get go. The Applicator table gives you other working options, not least of which is the underlit table (don't be greedy, nothing much bigger than 10x5), which I crave for precisely aligning prints onto ACM or Aluminium. Strangely, the leading brand is called Rolls-Roller, though I hear excellent things about Mounter's Mate tables and laminators.
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