The trendy looks in worktops are: square edges ... extra thick tops (70 - 100mm) ... or extra thin tops (10 - 20mm) - and, in laminates ... textured slate or granite lookalikes (textured to look like stone).
You'll find extra thick and square edged tops in relatively inexpensive laminates ... although concrete or quartz composites would be even more fashionable. You need to be careful, though, that the worktops don't end up uncomfortably high (with a new kitchen you can often adjust the plinth height a bit - but that would be more tricky with existing units).
Extra thin worktops are normally in quartz composite, stainless steel or glass - so would work out more pricey.
I don't think there's anything wrong with looking for something modern but, as Woody says ... make sure it's something you really like too. And I'd steer away from the very high gloss laminate worktops - they look stunning but they will get covered in little scratches, which you will be able to see when the light shines on them.
A 40mm, textured, granite lookalike laminate top, with squarish edges ... in a colour you really like ... would look very up to the minute on birch units, even if it wasn't truly trendy.