Where you start with plants, mulch first, plant second. Reason: mulching around plants takes a lot of time. Digging through mulch to plant, is a lot less work.
Where you start with small seeds, scratch the soil, plant seeds, keep weeding until plants are much taller than the mulch depth, then mulch. Mind you, I always lose a few when I mulch small plants afterwards.
When you start with large seeds (bulbs, potatoes, peas, beans), mulch first, or plant them and then mulch before they emerge. they will generally be able to push through mulch twice as thick as the seed length, unless it is matted. Grass clippings and certain deciduous leaves tend to mat.
Finally, the technique I use with medium seeds (such as beets or chard). I make my own seedless soil by sifting compost, I dig a hole through the mulch, I fill the hole with the sifted compost, and plant in there. You could do the same with storebought soil instead of compost.
As you can see I will do anything rather than go without mulch. The only thing I really seed directly on bare soil are certain small greens, lettuce and carrots, and even then I try to have clear plastic on the bed for a couple of weeks so as to make some weed seeds come up. If I plant perennial flowers (say, daisies), I always use the sifted compost technique. With weeds, it is easy to lose control.