When i first started i got by with chain lube, tyre pressure gauge(theres usually a compressor at the track), Hex key set (allen keys), Spark plug spanner, and normal set of spanners or ratchet, measuring tape for track of rear wheels. Then just oil and fuel to mix. I think thats about it! When looking at karts look for cracks in the frame, particularly under the seat or dodgey looking/flaking paintwork.
Most karters rebuild their engines fairly regularly, so check when last rebuild was done, and see if carbies clean and fuel filter used etc..