The two critical measurements are turbine shaft axial and radial end play. Axial play indicates hydrodynamic layer provided for thrust on the turbine shaft. Radial play indicates hydrodynamic layer provided for the CHRA (center housing rotating assy) to turbine shaft. These are actually the two working bearings located within the CHRA, the journal radial bearings and the thrust bearing (both wear parts included in a rebuild kit). Push/pull (shaft straight ahead with the face of the compressor or turbine wheel facing you) on the turbine shaft to measure axial; and lift up/down to measure radial play. Generally the amount of radial you will feel should be much greater than the axial/thrust play. Manufacturers have different specs so if you are using a dial indicator to verify you will need the service limitations from the manufacture.
Check the inside of the turbine housing for wet oil (soot is fine) that looks to be coming from behind the face of the turbine wheel. If there is enough oil to form a drip and run then the turbine seal rings are shot or on there way out. Same check on the compressor housing. These seals are wear parts included in a rebuild kit.
Check all the compressor and turbine fins for cracked/bent/broken. If the turbine fins are suspect walk away. The turbine shaft typically exceeds the MEL (cost prohibitive XA code). However compressor wheels are a viable replacement part and easily sourced. Factor this into the final price.
Check the compressor and turbine housings for cracked/bent/broken. If your turbo is internally gated check very closely around the WG (waste gate) flapper valve. Turbine housings like to crack at the WG valve seat (thin area). Turbine housings are also typically in excess of the MEL (cost prohibitive to replace XA-code) but not always, best to compare the price if needed against a new turbo. Compressor and turbine housings typically only suffer if the journal bearings wear out and allow the compressor/turbine wheel to contact the housing.
On the CHRA check all the threaded holes. Sometimes the pressurized oil inlet is NPT and sometimes its a fitting with a flange and a couple bolts. The outlet is typically flanged with a couple bolt holes. Check out the tapped threads on both sides. CHRA is typically a XA part (not economical to replace, buy a new turbo).
If you can source a turbo that is component balanced (like a Holset) you can easily rebuild yourself. Rebuilding assy balanced is not much harder, just carefully match mark the dynamic assy. Not sure about the old GM turbo's but chances are kits are available and rebuilding yourself is a breeze. If you can build a motor you can certainly build a turbo and save a bunch of money.