Most grills come on a cart made of steel and put together with nuts and bolts. If you don't feel particularly handy, most retailers will put the grill together for you for a small fee. At the higher end are stainless steel grills with welded joints and full axle wheels to facilitate movement.
You will need some cart real estate for holding food and utensils. Most carts have at least a folding or stationary side tray as well as one in the front. Wood shelves will deteriorate rather quickly. The more durable shelves are cast aluminum or stainless steel. Look for an interior rack for keeping food warm, a lid (for protection and maintaining a cooking temperature) and firebox made of stainless steel or porcelain-coated steel for durability.
As you step up the cooking chain, you may want to consider other options such as an electric rotisserie, a fuel gauge, griddle pan or even a smoker drawer and high heat infrared burners.
Look for an ignition knob or button that produces a couple of sparks (better yet an electronic igniter powered by a battery that produces continuous sparks)
when turned or pushed.
As you assess your needs and preferences, keep in mind size, fuel, taste and added amenities.