Before the yeast is pitched the wort should be aerated. The brewer can shake, splash or use an aquarium pump to dissolve oxygen into the wort. This is essential for proper yeast propagation and complete fermentation. Make sure it's not too hot or cold for the yeast to do their job.
Lag time can be different for all batches, but one should generally see airlock activity within 24 hours, but the activity isn't a sure sign of fermentation. Use your hydrometer to confirm fermentation activity. It can take longer for the yeast to start, but there are many factors. As for the airlock, I would recommend one as this is your first batch, but you can ferment without one, which is what I do.
The best advice I can give you is to relax and let the yeast do its magic.