Fluff and Personality
Perhaps the most intriguing part of the AM is the fact that they recruit from so many worlds, each unique in its own right and as such the individuals hailing from those worlds vary wildly. GW and Forge World sell models from several different sub-factions to match the breadth of human societies in the galaxy, be they the Tallarn sand raiders, the Vostroyan nobles, Valhallan ice warriors, Catachan jungle fighters, The Death Korps of Krieg, or the humble Cadian soldier. The immensity of the galaxy and the relatively haphazard record keeping of the imperium means you certainly can create your own unique world, society, and people to draw upon for your own regiment which really allows for you to customize and personalize your force.
The Astra Militarum also draws upon other sources, notably the Commissars who act in a commanding role. Trained nearly from birth for their role, they act as frontline commanders and morale boosters - though their way of boosting morale tends towards 'inspiration through fear'. In order to keep their men in line and fighting fit, they often must threaten to execute those found wanting, and in-game actually do execute soldiers who break morale and flee. Despite the barbarity of the technique it appears to work well enough and while the commissars are not generally liked or respected by their men, they get the job done and as such are a staple of any Imperial Guard regiment.
Additionally they draw upon other elite units such as the Tempestus Scions or Elysian Drop troops, the former of which recently got its own models line and supplement for gameplay. Stormtrooper-like in appearance, these better trained and better equipped soldiers are more effective than the common soldier, though they die almost as readily. As artillery shells scream overhead and and crack of lasgun fire floods the field, the attitude seems to be 'Die for The Emperor or Die Trying', and the Astra Militarum rarely disappoints in that regard. If none of this is cool enough for you, keep in mind that they can ride cavalry too, and what's more fun than charging horsemen into a pack of demons?
AestheticSeeing how many different regiments are available, there isn't really a unified aesthetic to the Imperial Guard aside from the presence of lightly armored and lightly armed infantry surrounded by heavy tanks. The general standard would be to focus on the Cadians, since they feature most prominently in art, fluff, and models lines coming out of Games Workshop. If you think of a combination of World War II militaries interspersed with elements from Starship Troopers (the film, not the book), then you will have a pretty close idea.
The vehicles themselves look decidedly 'pre-modern', in part because of the intentional World Wars/Vietnam War appearance, and in part because in the galaxy of the 41st millennium technology is pretty reverted in some areas. Sure, we have the capacity to travel the stars, shoot lasers, and colonize dangerous worlds, but we've forgotten how to give vehicles anti-gravity fields or aerodynamic designs. The models themselves generally have a fair amount of exposed skin, particularly in the face, so if that sounds like a daunting task then perhaps you might want to stay away from AM or select models from one of the different types of Imperial Guardsmen. However, for those who have skill in painting, the fact that these models are human and have faces you can see presents an opportunity to paint some really evocative miniatures.
In regards to the actual unit selection available, you can generally design your force in a few different ways to fit your playstyle. The Astra Militarum is capable of playing a horde style force with dozens of guardsmen on the field if you like outnumbering your opponent, giving them too many bodies to reasonable deal with. You can become the tank commander your childhood self only dreamed of and run columns of vehicles across your enemies' lines like every true treadhead desires. Or, you could channel your inner Top Gun and bring in the air cavalry, bringing more flyers to the table than any other army could hope to muster, and more than most could hope to take down. Neither are you restricted to selecting a single form of these general playstyles, you can mix and match the pieces you like and create a force that is truly your own. What they lack in physical strength or weapon skill, the men and women of The Guard more than make up for it in sheer will and numbers. As long as assault and close combat aren't something that you aspire to focus on, the AM likely have something for you.
How does that sound, soldier? Ready to defend the Imperium and fight for the continued existence of mankind? Grab a lasgun and let's get to work!