Safety and convenience are certainly served by keeping the shop clean. You may even find that a broom-cleaned space is a pleasure to come back to.
In any case, you’ll need a broom, a dustpan and brush, and a short-handled workbench brush. A shop broom with a wide brush works wonders in a large shop, though a traditional flat broom suffices nicely, especially in a smaller space. Don’t be tempted to add your sweepings to the pile under the table saw; it accumulates quite fast enough on its own. Bend down a moment, dustpan in hand, and get the dust up.
A whisk broom or other work-bench brush is invaluable when doing bench top work with the likes of planes, chisels, or routers. A flick of the broom now and again, on or around the workpiece, makes examining your progress much, much easier.
A shop vacuum is a useful investment for the workshop of some size. It will make cleaning up sawdust and miscellaneous debris easier, of course, but the good ones have the power to pick up glass and even shards of concrete. Some convert to blowers, too.
Unless your shop is very large, don’t buy a giant shop vac. A sixteen-gallon model is probably large enough. Be sure to buy a wet/dry machine. It will prove its worth for cleaning up spills and minor floods—in the house and workshop alike.