Starting with the body, think outside the norm. The shell will need to be ultra light, and good aerodynamics are far more important than your wheel resistance. You may want to research the Dacron covered
Geodesic Airolite Boats. Some of the boats are as light as 8 pounds. Yes. A row boar that weighs as much as your shoes! The principles involved in building them would work well for building an aero shell within your budget.
Motor depends on the course. a hub motor would win on a constant speed track, but if you have to accelerate and break, then a geared system would likely be of some advantage.
Tire choice depends on wheel choice, and that depends much on the other aspects of the design. Counterintuitivly, many manufactures have found and published data showing a wider tire has less rolling resistance. however, they do have more air resistance. There is also a huge amount of variance in rolling resistance based on things like tire pressure, rubber compounds, and TPI.
Higher pressure rolls with less resistance over smooth surfaces, but lower pressure will role better over rough surfaces. Harder compounds can have less rolling resistance, but if you need the vehicle to handle in corners, or stop under racing conditions, a softer compound might be better. Threads per Inch (TPI) counts over 300 are very siuple, and have a lower resistance, but the higher the TPI, the more prone to damage the wheel can be from road debris and rough road conditions.
etc, etc , etc.
Larger diameter wheels roll with less resistance, but cause more wind resistance.