"What if the client's budget is real tight? Are there some reasonable assumptions that could be made to develop a recommendation for repairs and overlay?"
You, and the Owner's first discussion should be about liability. If he wants to take on all the liability for future failures of these new repairs, then state that in your contract and give the owner a design that in your professional opinion is addressing the site conditions while optimizing the money he spends. If he says something like "you're the engineer, I'm paying you to design this right. It better work." Then you reply, "without information such as trench compaction, existing depth of asphalt, etc., I cannot determine the "right" design." The Owner needs to realize that it costs money to get someone to take on the liability for this kind of project. But if the Owner didn't have the knowledge to get the trench compaction tested during construction, it might be hard to get him to listen.
Cracks in the surface indicate a potential problem with the subgrade, which is why you want a core sample (as mentioned above). This core sample and proposed asphalt design from a geotech engineer should be less than $1,000. If the Owner doesn't want to pay this, then he needs to be prepared to take on the liability on his own, as discussed above. The Owner also needs to be prepared to find out that the pavement design from the geotech might require that he places more asphalt than he was prepared to pay for. Lastly, he needs to pay the geotech to be on-site during construction to test materials as they are placed.
If the Owner is reasonable, and will not hold you liable, then for design purposes, go with a 1-1/2" asphalt overlay as a minimum thickness. If the Owner wants to go cheap, you could also talk to contractors about other surfacing options like chip-seal. Make sure you seal the cracks and compact the trench prior to overlaying. If the water line is not very deep, the trench compaction efforts should be done carefully.
Good luck.