The lower the orbit, the higher the drag. Since the drag force is roughly proportional to area, but the resulting acceleration is force divided by mass, then the denser the spacecraft, the less it is affected by drag.
The simplest way to fight drag is to carry a lot of fuel, and use it often. This will make the spacecraft less dense as the tank empties, but also lighter and thus have less mass to accelerate by the same fuel, in a way that cancels out. The main thing to worry about is just that you have finite fuel, and thus will eventually run out and have no remaining way to prevent eventual decay.
Drag models of spacecraft are almost always spheres, but you could try making a long, narrow vehicle -- that is, rocket-shaped -- and keeping the nose oriented into the direction of travel. This will reduce drag, but if your vehicle has one end heavier than the other, then the gravity gradient will tend to pull it upright, so that its long side faces into the wind, thus increasing drag, and pointing the tail engine in the wrong direction. You will have to monitor attitude, and have additional thrusters oriented properly to correct it.
You could do very interesting things by designing the body so that it generates lift as well as drag, and maintaining attitude like an aircraft.
This is tricky to get right and requires a lot more fluid dynamics for proper modeling than is usually done, so you will need custom software to control it.
Also, drag is friction, which heats the spacecraft. The lower you go, and the more drag you encounter, the faster things heat up. You need ways to control that heat, and get rid of it, or your very low altitude spacecraft may melt long before it runs out of fuel.