Right away after your purchase
1) Mechanic: Visit your known mechanic to do a oil change, air filter, Fuel Filter change no matter what is the reading in the ODO. It wont cost a lot. but if you do. your car will be happy.
2) Tire shop: Usually if the car got maintained properly, the tires will tell. If the wear is uneven, then you may need to check the suspension or some alignments. Even if the tyres are good and evenly worn, do a wheel balancing.
3) Interior: I usually remove the carpet and vacuum thoroughly to remove small dusts settled in the carpet. Your cabin will feel fresh if you do it.
4)Air conditioner: Check the refrigerant condition and pressure. Let the mechanic decide what to do. If you run the car without proper level of refrigerant you may run-in to the risk of spoiling your AC compressor.
5) Check the battery and get it replaced if needed.
6)Anything minor, do it when the time you are taking delivery. Your car will run better.