He has 2 possible options for keeping current lenses:
If Minolta Maxxum/Dyxum/Autofocus lenses: Any Sony DSLR body will be fully compatible, and will meter, autofocus, and work like normal. All lenses will be stabilized as this resides in the camera body.
If his 35mm lenses are of the older MD manual focus variety, then the Sony bodies would not be the best choice. In this case, adapters are going to be needed for any camera you choose. As it happens, the best cameras to use old manual lenses with via adapters are the mirrorless cameras - Sony NEX, Olympus Pen, Panasonic G, and Samsung NX. All of these mirrorless systems have very small registration distances to their sensors and need only a very simple glassless adapter ring to mount any manual lens you want. The Sony NEX and Samsung NX both use an APS-C sensor and have the same 1.5x crop factor as most entry level DSLRs. The Olympus and Panasonic mirrorless cameras use a 'micro 4:3' sensor which is slightly smaller, and have a larger 2x crop factor.
Some DSLRs might be able to use the Minolta lenses via adapter, but may not be optimal to use them - often the adapters have glass elements in them which reduce quality, some have trouble with infinity focus, and you have to have very good lenses to make it worthwhile. If his old Minolta glass is really good stuff - the real high end lenses that people would still love to have, then it's worthwhile. If his Minolta lenses are kit lenses or basic cheap zooms, then it might not be all that important to try to adapt them.
Do you happen to know what the lenses are? Those of us familiar with Minolta lenses can tell you how good or valuable any of them might be, and whether it's worth it going with a Sony DSLR system, a mirrorless system, or just scrapping them and not worrying.